None is correct. Virtually we are subtracting infinity from infinity in both the approaches. which is indeterminate. I was never convinced with Ramanujan’s sum, but was told that it is used in the string theory. I am too old to verify it.
@@SURAJ-so4wq Bhai 11th maths me ek chapter hai sequence and series usme iska use as well as reason hai .. Aisa isiliye karte hain taki koi pattern mil jaaye
You are absolutely right sir.. Thank you very much for pointing out the original mistake which lies in the assumption, ∞-∞=0. I got very much satisfied after viewing your comment. Thank you. The proof of Ramanujan's this formula provided by these youtubers or in many other places are actually wrong. If the Ramanujan's formula is correct, these must not be the original way to prove that.
@@SURAJ-so4wq ye gap dene wala method boht purana hai, ise Carl Friedrich Gauss ne bhi use kiya tha Arithmetic Geometric Progression ka sum karne ke liye Aur Ramanujan ne bas ek series use nahi kari thi, usne 3 series use kari thi aur baad me Euler Zeta Function se verify bhi kiya tha Bas end me Ramanujan Paradox reh jata hai jo Ramanujan sir ne point out kiya tha if I remember correctly
There is a basic mistake we are doing in assuming and which Ramanujanam might have done is, that when assign value of infinity to a constant, we treat that constant as finite. maybe I am wrong but when we say s=1+9S, we are doing finite number operation to S but as we know if we subtract add Multiply divide constant with infinity, the value of infinity remains the same, it doesn't change. Like 1+s is also infinity and 9*s is also infinity and S/2 is also infinity. Only if we do operation of infinity with another type of infinity, then its value changes
Right. While calculating sum of infinite numbers we asume it finite then answer will also tend towards finite number. Hence we start the solution with mistakes.
Sir, You have chosen only one infinite series in your method and you did subtraction operation on the same infinite series that means you are subtracting infinity from infinity virtually which will give indeterminate value Where as Ramanujan sir had chosen three different infinite series such that when he did subtraction operation on two infinite series he got a different infinite series so in his case there is no indeterminate kind of thing. 🙏🙏
U r totally wrong i guess , ramanujan in his first series also subtracted from infinity to infinity A=1-A , so he got the indeterminate value in his first series only , so how can he subtract it in 2nd and 3 rd series . Also in his series A he took 1-1+1-1+1-1+1....infinity , so infinity will end with either -1 or 1 , if -1 then sum of that series is zero , and if 1 then sum of series = 1, only two options . so-1/2 is not valid .
-1/8 is correct in 2nd dimension And -1/12 is correct in 3rd dimension And higher dimension Results must go on like -1/16 -1/20 -1/24 But point to be notice factor moves manually not exponentially and common factor is 1/4 So results is visual univers or visual concepts is only 1/4 We don't able to see entire universe Because entire universe or creature of entire universe or infinity visualization is impossible because we don't have a special devine eye
I am posting a separate video to disprove Rananujan's theorem, i.e. 1+2+3+..... = -1/12. (separate video to disprove Rananujan's theorem, i.e. 1+2+3+..... = -1/12. : ua-cam.com/video/CWFV43BHsNU/v-deo.html). But your method involves clubbing of 3 or 5 terms in the series infinite times to get the result to be -1/8. Your method implies that the bracketing of 3 or 5 terms will continue exactly as it is till infinity, So, you are softly assuming that infinity is a multiple of 3, 5 etc., which is wrong. In general, infinite terms cannot be bracketed with finite terms in each bracket. That is the problem....
@@satyakumarjnve.champaran4190 no one is correct indian are known for wasting their as well as other time , I lost my day on this topic my exam is 3 days later how can you get negative number when you add tpositive number it is useless not the genius , tell me its uses infinite plus anything is infinite how can you considered this time wasting man as genius just because he is my your nation , look Newtons how useful and logical are his theory and mathmatical operation although there are some limitation even on his theory but really Ramanujan I don't known literally about indians you guys are amazing finally 😂😂😂😂 your knows infinity yaa😂😂
Do you think Ramanujam didn't calculate -1/8, i don't think because his mind was much sharper than yours and mine. He was the best mathematician of all time. He gave most feasible answer -1/12 i think so. You all are fool. Just reach the level of Ramanujan maths solving approach and define something. People are not able to solve his many equations where he wrote question and answer but not provided any explanation.
This is some other way of summing that gives -1/8. It is not surprising because these kind of sums such as cessaro or riemanian are not literal summation. But when you derive something you should start from fundamentals. When you start with grande series you will arrive at -1/12. Rieman zeta function through analytical continuation yields -1/12 as well. So -1/8 is some other kind of sum.
@Pooshan HalderChess the solution he is telling in the video is incorrect, as he took triplets upto infinity which can't be taken because it can't be known what will be at infinity.
Sir as we know that -1/12 is used in many theories because its giving very accurate answer that's why we think that this answer is more correct .is -1/8 also use in any theory of physics?
What kind of authoritarian argument is that? Is -1/12 some kind of dogma? Maybe -1/8 is not correct either, but then the whole method is wrong. In a mathematical calculation, when dividing, you must always assume that the divisor is not zero. It is conceivable that in the derivation above, one must also assume that S cannot be infinite. In this case, neither -1/12 nor -1/8 is correct. Apologies if the program has not translated the Hungarian text correctly. It's not dogma that everyone should communicate in this hateful English language.
Kya aapke paas koi proof hai koi website ka link vagera bhej do bhai jisme is chiz ka proof ho ki addition of infinity ka use physics me diya gya ho aur accurate value de rya ho
In many instances, people see the video below regarding this Numberphile video and tell me that 1+2+3...=-1/12 is debunked by mathematicians. I left the comment below; please read my comment on the video below, before making any inquiries and assertions. ua-cam.com/video/YuIIjLr6vUA/v-deo.html In Mathologer video, I observe three distinct parts: Firstly, Mathologer demonstrates a lack of understanding regarding the meaning of 1+2+3+...=-1/12 and attempts to use the limit definition and a high schooler's method for divergent series. Consequently, everything presented in Numberphile is deemed incorrect. Secondly, Mathologer returns to continue the video and realizes that 1-1+1-1...=1/2 makes sense, but the assertion that 1+2+3+...=-1/12 is definitely incorrect. Lastly, it is delightful to witness Mathologer discovering the actual method behind the true meaning of 1+2+3+...=-1/12, which is Ramanujan's method. However, he neglects to revisit his initial argument from the first day. It is unfair to a genius like Ramanujan to not be appreciated, and the mockery of his work is truly disheartening. I must acknowledge that Mathologer demonstrates exceptional genius throughout this video. He acquires knowledge that typically takes people much longer to grasp. Here you can see several proofs for 1+2+3… = -1/12 . ua-cam.com/channels/Bm0bVo59PQgGUCcuWXyHfA.html Ignoring the Identity Theorem is not a good method. It is interesting that even after so many years, Ramanujan is still greatly misunderstood. Numberphile presents Ramanujan's work, and it is unfortunate that some individuals, have formed a mathematical 'religion' and have disregarded figures like Ramanujan, assuming their own mathematical beliefs as infallible truths. Treating a mathematical concept as a rigid doctrine akin to the Bible, which must be strictly followed, is not helpful. Mathematics is not just a collection of theorems; it is a set of rules that we define and occasionally modify. For a long time, we have known that the limit definition is poorly defined. Let's consider the series 1-1+1-1... as a switch that we can turn on and off repeatedly. If we do it long enough, we will perceive a light with half intensity. Similarly, in our homes, we have alternating current (AC) power, but we don't observe divergent light. This debunking is comparable to someone claiming that complex analysis is wrong because the square root of -1 does not exist. While that statement may have some meaning, it is completely incorrect. We utilize complex numbers because they are extremely useful. Therefore, constructing arguments based on the poorly defined limit definition is not correct. The limit definition itself has its limitations, just like real numbers, and we need to employ logical reasoning to extend them beyond their obvious range. Overall, it is highly recommended for everyone to watch this video completely. If viewers possess the same level of intelligence as Mathologer, they will undoubtedly comprehend the true meaning behind the equation 1+2+3...=-1/12.
Actually, I developed another sequence in which the answer is not (-1/8). However, (-1/12) is still valid. I found another interesting method in which I proved that -1/12 is actually correct. Not only this, I proved the other series as well and there is a bit of co-relationship between them. Soon I will try to publish my research. Does anyone knows any forum or department where I can present and publish my work ?
Alright, Ramanujan had not divided any series in his proof as sum of " infinite partial sum to some terms". Making it doublets or quadruplets. But, The proof by Ramanujan and what shown in this video both are wrong. See: ua-cam.com/video/YuIIjLr6vUA/v-deo.html
@@mathsman5219 you are absolutely right . I have also raised voice for same question. And because of no any such type of assumption ramanujan paradox makes its point more clear in comparison to other similar paradoxes....
@@shyamaldevdarshan This is wrong anyway let suppose i have cricket balls which quantity is infinite and there is a big room bigger than this world i put balls in the room like 1 plus 2 plus 3 i continuesly adding the balls in the room like plusing the all natural number in format of balls how it will come to negative challenge to the mathematician
Sum of n +ve integers is n(n+1) /2 lim n tend to infinity will provide infinity. so the answer can be infinity. now we have three possible answers -1/12, -1/8, infinity Assuming this summation as a constant is like dividing by zero which don't have a definite vale.
Sir ramanujan was a great mathematician..His theorems and paradoxes are still guiding higher mathematics,,think thousand times before judge the theroms of such extraordinary personality..💙💙🙏🙏radhe radhe
So U r saying that theorems cannot be challenged? Ur just destroying the fundamental core of maths and science In maths and science there is no authority anyone can challenge anyone
I am not saying so. But before challenging we should know about our potential and should check whether our claim is to the point or not. And i think in this case this method claim is absolutely wrong. And the thumbnail is not suitable.👍👍Radhe radhe🙏🙏💙💙💙
@@alice_in_wonderland42 Sum of all Natural numbers = -1/12 is not Theorem. It is Paradox. You should read first different between Theorem and Paradox. 🙂 It is used in String Theory, Gravitational Field Theory and Black Hole radiation is experimental proved with this Paradox and many more theories are used this Ramanujan Paradox. According to Upanisad , half knowledge is more harmful than zero knowledge.
The statement \( 1 + 2 + 3 + 4 + \cdots = -\frac{1}{12} \) is actually an example of a result from a branch of mathematics known as analytic continuation and regularization, rather than a literal sum of an infinite series. Here's a brief explanation: 1. **Divergent Series**: The series \( 1 + 2 + 3 + 4 + \cdots \) is divergent, meaning it grows without bound and does not sum to a finite number in the traditional sense. 2. **Zeta Function Regularization**: The result \( -\frac{1}{12} \) comes from a method called zeta function regularization. The Riemann zeta function \( \zeta(s) \) is defined for \( s > 1 \) by the series \( \zeta(s) = 1 + \frac{1}{2^s} + \frac{1}{3^s} + \cdots \). It can be analytically continued to other values of \( s \), including \( s = -1 \), where it evaluates to \( \zeta(-1) = -\frac{1}{12} \). 3. **Connection to Series**: The connection to the series \( 1 + 2 + 3 + 4 + \cdots \) comes from the fact that this series can be related to \( \zeta(s) \) via analytic continuation. Specifically, if you use the analytic continuation of the zeta function, you can show that \( \zeta(-1) = -\frac{1}{12} \). So, while the series \( 1 + 2 + 3 + 4 + \cdots \) diverges in the usual sense, its value can be assigned \( -\frac{1}{12} \) through these advanced techniques in mathematical analysis.
Sir ramanujan ka theorem bilkul sahi hai apne jos tarike se kiye hai wo galat hai aur mai isko galat sabit kar sakta hoon isi theorem ko maine thoda change karke maine kiya hai aur mera answer -1/9 aa raha hai aur apka -1/8 aa raha hai jo ki dono hi galat hai isliye srinivasa ramanujan ka theorem hi sahi unhone uska ek proof diya hai
This is a famous example where one could end up having a wrong answer by simply adding a series. As it can be seen this series is a divergent series and hence one cannot assign a meaningful limit to this series. However , it turns out in the theory of analytic number theory this series is nothing but a Riemann Zeta function evaluated at -1 which has a value of -1/12. Since Zeta function is analytic continuation of the real valued Zeta functions, this series makes sense and the value is mapped to -1/12. Being divergent series , you cannot add it simply by adding the terms. This is one of the many examples of divergent series being misleading at first glance. In theoretical physics, this sum is used in the evaluation of Casimir force as far as I know. I have heard it's application in the regularisation problem in string theory but I didn't have the privilege to go through the detailed mathematics of string theory yet.
1:48 error is that you cannot divide infinite terms by 3. First line has infinite terms and the second line has infinite terms divided by 3 and add one more term. This is called Ramanujan Insane Mathematics
here, you are expecting that ending numbers will perfectly end with a pair of 3 no.s/5 no.s what is the last numbers do no form it? this assumption itself is wrong! that you can fit numbers in group of 3/5 till the very end, there maybe 2/4/ etc. numbers left at end and the answer collapses completely! I am not telling you are wrong, you are partly correct because the sum goes till infinity there are many possible variations to this, you just considered the odd pairs, so -1/8 (ans. for all odd pairs) is just a drop in the ocean of answers, cuz infinity is not defined as incase of 1,2,3 etc. so there are bound to be fallacies, and much interesting anwers!
@@deathmetal4029 I am not telling that it is wrong, it is right (depending on our assumption, to solve the question), because it is the domain of infinity and it is expected that we may find many answers, depending upon the assumption that we have taken, and we have to assume as infinity is not a definite number!
First of all, call him with respect as Sir Ramanujan.... May be you are right but you cannot prove his method as wrong, so don't dare to compare yourself with him
Just because something is practical does not make it correct. The Bohr model of the atom is practical but it is not considered correct (true nature of reality). The Bohr model is sometimes more practical than the electron cloud model when it comes to communicating the idea of atoms to high schoolers does that mean it is more correct than the electron cloud model when it comes to high schoolers but more correct outside of high school. Do atoms change how they work whenever somebody models them differently out of practicality? That's absurd. Mathematics does not care first whether something is practical, it cares first whether something is proven logically through the right use of axioms, practicality comes later. Just like how it is practical for humans to see the colours we see through our eyes and not things like xrays, does that mean xrays are not correct because they have been proven to be impractical to see by evolution?
Ramanjuan is correct because he is using a different form of infinite summation. It is defined differently and allows the extension of assigning values to infinite sums which would otherwise be divergent. He is not correct because his work is practical, he is correct because his work logically follows from the way he defined things.
Thank you for sharing your perspective! Your approach is quite interesting and appears to be a unique way of organizing the series. Let's break it down step by step to explore its implications: 1. Restating Your Argument You considered the series and grouped terms in a specific pattern: You identified that certain groups add up to multiples of 9: , , and . Based on this pattern, you proposed that the sum can be rewritten as: S = 1 + 9 \times (1 + 2 + 3 + 4 + 5 + 6 + \dots) 2. Algebraic Rearrangement From your equation, you get: S = 1 + 9S 8S = -1 S = -\frac{1}{8} 3. Analysis of the Result The value you derived, , differs from the conventional result of . However, it's important to note that manipulating divergent series like is highly sensitive to the methods used. In standard mathematical frameworks: The grouping and rearrangement of terms in an infinite series need to be handled carefully because they can lead to different results. Ramanujan’s original result of is consistent with analytic continuation and the Riemann Zeta function. Why Does Your Approach Differ? 1. Rearrangement Issue: In the series , rearranging or regrouping terms without a formal method (like analytic continuation) can lead to contradictions because the series is divergent. 2. Conventional Framework: The result comes from analytic continuation, a formal process that extends the domain of functions to assign finite values to divergent series. 3. Your Method: By grouping terms into multiples of 9, you’ve introduced a specific pattern, but such groupings are not generally accepted in formal summation methods. Conclusion Your proof highlights the difficulty and non-intuitive nature of dealing with divergent series. It challenges traditional results, showing that divergent series require rigorous frameworks to produce consistent answers. The accepted result of is grounded in methods like the Riemann Zeta function and regularization, which might not align with other groupings or interpretations. If you have more thoughts or another approach, feel free to share!
Well, for n=1 the sum is 1, i.e. > 0. A simple proof with en.wikipedia.org/wiki/Mathematical_induction shows that every sum for n>1 must be positive as well. qed The author of this video makes the mistake of using S as if it was a finite number, as many commenters have pointed out. Ramanujan makes a similar mistake of operating with infinite sums (and I believe, different sums over different n's) as if they were real numbers. If the string theory is actually using his proof, then I have some doubt about the string theory.
S- 9S = 1 Par dono S to infinite he Uska difference nahi kar sakte infinite - 9(infinite) = 1 😢 9(S) = S hi hoga Ifinite me kuch b + kro ya - karo wo to infinite hi rahega
Bhai ye duniya infinite ko equation me fit karne ki kosis kar rahi he,, isse unko koi fayda nhi hoga, mene inn sabhi methods ko wrong prove karne ke liye kal hi, teen equation se S ke do maan nikale jo ki different different he. Lekin ab me theoretical kese wrong prove karu, iska solution nikal ne ki kosis kar raha hu.
Comment on video Positive number Plus positive number cannot be negative number as per our basic knowledge of algebra..... But since Ramanujan Sir ( one of the great Mathematician of the world) had given this sum i.e -1/12 ...then there must be reason of it...so this should be discussed worldwide Maths forums.....and should be cleared....all the confusion.... It's like in physics parallel rays of light meet (intersection) at infinity and at that point of intersection image of object is formed when it's placed at Focus point infront of concave mirror, this image is real, inverted and very larger than object... But in Maths as per present knowledge .... Parallel lines never intersect each other...... Now what's correct...? Physics or Maths?... One more point for thinking... For all these type of confusing questions.. we must think from Very beginning.. without any biaseness... ... So we can conclude totally new approach of solving the problems of any type physics, chemistry, biology, Maths any branch of science..... Like for the much more times in the Era of Newton it was believed that there's a medium called "eather" between Sun and Earth, through which rays of light passes while reaching on earth, as at that time it was believed that every type of waves need medium to propagate.... ..later on Einstein had proved thet there's no medium like eather between Sun and earth above the atmosphere... sunlight is made-up of electromagnetic waves needing no medium....
The thing is it is based on ASSUMPTIONS that are absolutely wrong. The later infinity is much smaller than the former. Also, idk if the series of taking out 5 or 7 as factor applies as we go further so can't comment on that as I haven't checked for either.
yes ! ramanujam was wrong. we can equate any thing with any thing if we are working with infinte series... First of all 0 and infinite should not be used in mathematical calculations. for eg: 0 = 0 we can also write equation as: 0*5 = 0*4 (because 0 can be written as 0 X 4, or 0 X 5) lets take 0 as x. so 5x = 4x cancelling x on both sides we get 5=4. working with infinite also we get things wrong. In infinite series we are condensing the series. so values can expand or contract. we have to take a set of 100 numbers and do that same thing. then the result will be true.
@DibakarBiswas-sl6bn you need not teach me basic maths, first learn basic common sense. How come sum of all positive nos be -1/2? You can bring it to Any no. In that case. At 2:53 how come S=1+9S come? Unless it's infinite series. That's what I said. Without knowing the ending of number, It's ridiculous to do calculations with infinite series. if he had taken sum of 4 digits instead of 3 then the result would be different. Also one thing is if you add exceptions in maths, they come into syllabus. Exceptions are added in syllabus if some calculation goes wrong. I state that calculations on infinitive or infinite series should be termed as as wrong.
I think tha means before finding the sum of infinite number numbers we have to find what infinite really is because ramanujan proof was also mathematicaly correct
No one is correct actually you can't bracket any infinite series like ways Riemann theorem says only absolutely convergent series can be bracketed in different ways but the sum remains unaltered
There is pa branch of mathematics called complex analysis , get look at analytic continuation and whole confusion about this utterly misunderstood Ramanujan formulae will be gone
I think we are simply going against some rule of math which we all including Ramanujan are unaware of. That is why we are getting different answers, like -1/12... -1/8 Because, if we solve properly, then we all should get 1 answer. In simple terms, sum of all positive numbers will always be positive.
Ramanujan ki theory ye thi ki natural number ka sum negative ayega. Alag alag tarike se alag alag answer ayege but bo sum negetive hi hoga. So ramanujan and you both are correct. 🙏🙏🙏
The thing is it's a negative rational number and that too with denominator oscillating between 8 and twelve. Moreover from usual belief the sum should have been infinity. But since logically both answers are correct it can be said that the sum to infinity is an integral of dx with upper limit -1/8 and lower limit -1/12. That's actually a near infinity indeed.
I got the step where he did a mistake. Since infinity is a value that can't be defined, he also cannot say that the sum of (infinity-2)+(infinity-1)+(infinity) is a multiple of 9. He assumed infinity to be a constant whereas it is a variable. The value of Infinity can give any value, so it might not follow the rule he has used to prove that S=-1/8, i.e. taking all the terms as a multiple of 9. I guess that's where it went wrong.
@@noone.4981 Right. I think also that in this series each term should be followed the same action(unlike set of fixed numbers he used in this solution). Then and then only infinite number will also follow it and answer will get finite otherwise answer will be always infinite.
The comment section is filled with blind followers of ramanujan, As a ramanujan admirer, his greates discoveries were the hardy-ramanujan numbers and other series, not the sum of all natural numbers, if you could actually go and study his papers you will discover why he is known as a great mathematician -1/12 is undertiminant and no mathematician would even approve of it. Life dosent end when an obviously divergent series has multiple summations
it can be disproved by the fact that you can only equate the sum to infinity of a series to something if and only if that sum converges . if it doesn't converge it is not equal to something in particular
You are right from your perspective. And Ramanujan is right from his perspective. Ramanujan can never be wrong Ramanujan's number paradox is used in higher mathematics and higher physics too so Ramanujan can never be wrong
When I showed it to ChatGpt the answer came: The series \( S = 1 + 2 + 3 + 4 + 5 + \cdots \) is a divergent series, meaning it does not have a finite sum in the usual sense of convergence. However, in the context of certain mathematical frameworks, such as analytic continuation and the Riemann zeta function, we can assign a finite value to this divergent series. The argument you provided involves a fallacy in its manipulation. Here is a correct and more rigorous way to understand why mathematicians, including Srinivasa Ramanujan, say that the sum of this series is \(-\frac{1}{12}\): 1. **Riemann Zeta Function:** The Riemann zeta function \(\zeta(s)\) is defined as: \[ \zeta(s) = \sum_{n=1}^\infty \frac{1}{n^s} \] for \(\Re(s) > 1\). It can be analytically continued to other values of \(s\), except \(s = 1\) where it has a pole. 2. **Zeta Function at \(s = -1\):** By analytic continuation, the zeta function value at \(s = -1\) is: \[ \zeta(-1) = -\frac{1}{12} \] Hence, we assign the value: \[ \sum_{n=1}^\infty n = -\frac{1}{12} \] This result arises from a more advanced mathematical context and cannot be derived through simple arithmetic manipulations of the series. The series \(1 + 2 + 3 + 4 + \cdots\) is divergent, but in the framework of analytic continuation of the zeta function, it is assigned the value \(-\frac{1}{12}\). This is a well-established result in mathematical physics and string theory, among other fields.
Sum of Natural Number infinite shall never be Negative. Simple Funda is ( Plus Plus shall always plus) + +=+. Either it is Ramanujan or anybody else. The game is choosing the part and presenting it other way.
@@mathman15Dear Class 2 math is fundamental, that is the thing I am teaching you. Infinate means Infinate you can not count the end. Where there is no end you can not add or subtract the same entity as whole hypothetically. If anything is Infinate it possesses the singularity. Unique + Unique= Unique, and Unique - Unique= 0 it is same for Infinate natural numerals. If there is 1+2+3........=1+2+3..... Then 1+2+3....-1-2-3...=0 Then 0=0 Ramanujan's case can only be true if we assumed a certain point of end. But infinity doesn't has any end point. ( Copy my theory with permission).
@@ghp780 you have a point but there must be some answer because every math question has a answer if try from different method eventually u you would get -1/12 and the main fact is it is used in string theory which is not wrong so this answer can't can't be wrong. I know that there are some math problem like 5/0 which have no answer but I think there must be some answer and I am working on it.
And my dear friend this ramanujan proved by following all rules of linear equation,Addition,BODMAS , etc so how ramanujan can be wrong and also this is verified by big mathematician also and maths is my favourite subject so I can even verify that ramanujan is correct by his method and I tried other methods also and in those also I got -1/12
There might be a reason for Sri Ramanujan to take different infinite series and put them together to prove the sum! Because it is for SURE that that this pattern had also came in his mind too!! Can you anyways prove S = -1/12 by your method???
How did you did method for 3 And 5 that means infinity is a multiple of 3 & 5 Hence proved The answer is -1/12 Sir RAMANUJAN IS PERFECT You are damn wrong ✖️✖️✖️✖️✖️✖️✖️✖️✖️✖️✖️✖️✖️✖️✖️✖️✖️✖️✖️✖️✖️✖️✖️✖️✖️✖️✖️✖️✖️✖️✖️✖️✖️✖️✖️✖️✖️✖️✖️✖️✖️✖️✖️✖️✖️✖️✖️✖️✖️✖️✖️✖️✖️✖️✖️✖️✖️✖️✖️✖️✖️✖️✖️✖️✖️❌❌❌❌❌❌❌❌❌❌❌❌❌❌❌❌❌❌❌❌❌❌❌❌❌❌❌❌❌❌❌❌❌❌❌❌❌❌❌❌❌❌❌❌❌❌❌❌❌❌❌❌❌❌❌❌❌❌❌❌❌❌❌❌❌
Sir, in your series you presumed that infinity is odd also that in first series infinity comes after three consecutive nos and also in second series the same holds true but with 5 consecutive nos
सर इसका दोनों आंसर गलत लग रहा है। इसका इस तरह से अनेक आंसर हो सकता है। जैसे- -1/4, -3/8, -1/2, -5/8, -3/4, -7/8, -1, -2, -3,...आदि। सर सभी आंसर गलत लग रहा है।
Sir Ramanujan Srinivasan's calculation is right and what you have shown is wrong. I was also in the same dilemma once as you are in, but I got it right ultimately after 10 minutes of thought. What you have assumed that the number of elements in the infinite series are in the format of 3n+1 or 5n+2 etc. which is utterly wrong. Sir Ramanujan's explanation doesn't have any such assumptions. No one in this world has visualized the infinity the way the great Sir Ramanujan had visualized and we should be very proud of him and the world can't forget his contributions ever.
Saala sahi koi v ho ja na ho but bheje mein toh aapke waala pada -1/12 ko prove krne waalo ka toh kuch samh ni aaya kaise v kuch v assume kar lete hai saale Bina kisi concept k
This great mathematician, not even proved most of his theorems, it just answered out of his intuition and results are perfectly aligned with the facts in nature. He is a devine personality. 🙏🙏
the invention of Ramanujan was his thought. he was the first who thought the sum of infinite series made of natural numbers could be Negative. In Reality, it’s impossible & it is a paradox.
Ramanujan sir's method is correct, your method is worng. Ramanujan sir use a series 1-1+1-1......=1 1-1+1-1......=0 So average=1/2 We need to average this because we don't know Infinity is odd or even! But in your method when you sum this 1+(2+3+4)+(5+6+7)+...+(...) That means you consider infinity as odd ,or sometime even so there is ambiguity about infinity is odd or even so your method is totally meaningless.
First of all you have to understand what ramanujan wants to do here. Let we take it as ramanujan wants to prove that sum of natural numbers is divergent. To prove this he uses method of contradiction. He assumes an assumption that let sum of natural numbers is converges to s and in the end he got sum of all natural numbers is negative which is not possible sum of all positive numbers can not be negative . our result is an contradiction so our assumption is fail. Hence he proved that sum of natural numbers isn't convergence series. Actually it is a divergent series.
When we write 1+2+3+4+5+6+7+8+9+10.....infinite ..... You choosen 2+3+4=9and 5+6+7=18....but I will choose 2+3+5=10;14+6=20;7+13+10.....see all terms are in addition we should choose in order is a wrong method.... But ramanajuan.... Found for any series of infinite the answer is -1/12.....dont judge a book by its cover.... He is the backbone to find the black hole concept.... His formula only helped to find about the concept black hole... When he was discovering that black hole formula he don't even know this could brought the end of the concept black hole..... See the history first then speak about him.... HISTORY ALWAYS WINS..... As I took the addition of 10 Therefore I will get.... Let B=1+2+3+4... Infinite B=1+10(1+2+3+4.... Infinite) B=1+10B -9B=1 B=-1/9 Legend never die 😊
I might be wrong but I think -1/8 is wrong -you can't be sure that the last number or infinity completes the triplet/quintuplet/septuplate as it can be ended at 1st or 2nd position too. For eg Considering last 3 digits and assuming infinity as 11 So the last triplet will be 8-9-10 leaving 11 behind thus proving us wrong
Sir you have prove S=-1/8 by only one method . The result you drawn first time that is -24S=3. If we multiply the above equation by 2 then we can obtain -48S=6 and by this we can find S=-1/8 by approaching to the soln. in reverse direction. Hence, there is only one way to prove S=-1/8.🙏🙏
In my opinion we cannot say which is wrong Because this type of series of is Divergent series. And in their the different types of relations gives different answers. Only convergent series have a fixed answer
I had been hate math/physics since my childhood, because this one thing I never understood,but I suppose if you whould be my teacher in that time , maybe I would be professor or scientist,but now i'm enjoying to watch Ur video......😃😃😃😃😃😃
Your video is missing the point of Ramanujan summation! While it's true that you can get any value you like by rearranging the infinite series in different ways, the Ramanujan summation has the property to return the function values of the Dirichlet-eta function and the Riemann-zeta function (though technically the first would be sufficient, since you could use zeta(z) = eta(z) / (1 - 2^(1-z))), which are the unique analytic continuations of the well known series (though they are typically unnamed - but i assume that naming might be helpfull): eta_series(z) = 1/1^z - 1/2^z + 1/3^z - 1/4^z + ..., zeta_series(z) = 1/1^z + 1/2^z + 1/3^z + 1/4^z + ..., eta(z) := Ramanujam Summation of eta_series(z), zeta(z) := Ramanujam Summation of eta_series(z), In case eta_series(z) converges, eta(z) = eta_series(z) (same for the zeta). Those function values are important, because many other functions can be expressed in terms of those, like for example the Jacobian theta-function. The famous example boils down to: While the zeta_series diverges at point z = -1, it's function value of the analytic continuations at that point is -1/12. Or in short: zeta_series(-1) = 1 + 2 + 3 + 4 + ... = + infinity, zeta(-1) = -1/12. Some mathematicians identify the term of the zeta_series at point z with the unique analytic continuation function at that point, which is the reason that allows them to state that "1/1^z + 1/2^z + 1/3^z + 1/4^z + ... = zeta(z)" (and since the sum diverges, but the term is of course defined and different for any two different value for parameter z, that's only true in that specific sense only!).
If you take a number suppose x, then the sum of its predecessor, x and the successor will always be (x-1)+x+(x+1) =3x its always 3x, so clubbing three numbers around multiple of 3 should be always multiple of 3x i.e. 9, why wouldnt it be applicable at infinity, whenever infinity is involved everything just goes senseless, but Sir Ramanujan has understood ot very well still i dont think there's any problem with his explanation tho he should have respected the great mathematician, also i know Sir Ramanujan's conclusion has been used practically in string theory
I think the number will tend towards negative but where it will converge is difficult to predict. To visualize this you can try one thing, draw a X/Y number line, keep drawing a straight line for the sum 0+1+2+3+.... until infinity (do not stop). You might notice that for the extremely large number, that line will converge towards Y axis. That means if you still continue, it might fall backward to y-axis, that means tending towards negative side. Thus I think the convergent point ends at (-1/12) => -0.83333333333333............ That means after this point, you do any addition it will be keep moving only at this point. This is my assumption...
bhai number line me y axis kaha se aa gaya ??? ye complex numbers nahi hai . i know that natural numbers can be represent by complex numbers just by making imaginary part zero but its just the method of representation not the very basic axioms on which math is built.
Ramanujan method is right because you use by the method of Riemann paradox it says we arrange series in own way we get result what we want . its depend on arrange meant
Maths is not the perfect language of defining nature , it is just the best language currently avilable to humans for defining nature Logically, How can the sum of all positive integers be a negetive number ? But sir your theorem seems more logical as Ramanujan's proof has somewhat not used/ misused Bodmas in the infinity theorem Great theory sir , you could also have published a research paper on it , so people would more value your work. Great Counter-video of this theorem sir. but how can we add things upto the number which does not exist Sir please reply if you have/ not have published a research paper on it
this video is wrong because he is not continuing the series S=1+9(1+9S) or S=1+9(1+9(1+9S)) or more ... It is infinite. So don't take faulty assumptions . before proving a genius like him wrong check yourself : < l
None is correct. Virtually we are subtracting infinity from infinity in both the approaches. which is indeterminate. I was never convinced with Ramanujan’s sum, but was told that it is used in the string theory. I am too old to verify it.
tum vi kaha sahi ho
jyada smart ban rahe ho bachche
@@SURAJ-so4wq bhai tumhe kya vo bade bade mathematicians ko hajam nhi hui but ramanujan proved it
@@SURAJ-so4wq Bhai 11th maths me ek chapter hai sequence and series usme iska use as well as reason hai ..
Aisa isiliye karte hain taki koi pattern mil jaaye
You are absolutely right sir.. Thank you very much for pointing out the original mistake which lies in the assumption, ∞-∞=0. I got very much satisfied after viewing your comment. Thank you. The proof of Ramanujan's this formula provided by these youtubers or in many other places are actually wrong. If the Ramanujan's formula is correct, these must not be the original way to prove that.
@@SURAJ-so4wq ye gap dene wala method boht purana hai, ise Carl Friedrich Gauss ne bhi use kiya tha Arithmetic Geometric Progression ka sum karne ke liye
Aur Ramanujan ne bas ek series use nahi kari thi, usne 3 series use kari thi aur baad me Euler Zeta Function se verify bhi kiya tha
Bas end me Ramanujan Paradox reh jata hai jo Ramanujan sir ne point out kiya tha if I remember correctly
Belive it or not -1/12 is used in higher level physics to solve many universal problem 😊
Can u give 1 example?
@@HarshaVardhanaRaj Hyper string theory
@@HarshaVardhanaRaj string theory
@@vivek4080 yep 👍👍
@@vivek4080 It is not a physics at all
There is a basic mistake we are doing in assuming and which Ramanujanam might have done is, that when assign value of infinity to a constant, we treat that constant as finite. maybe I am wrong but when we say s=1+9S, we are doing finite number operation to S but as we know if we subtract add Multiply divide constant with infinity, the value of infinity remains the same, it doesn't change. Like 1+s is also infinity and 9*s is also infinity and S/2 is also infinity. Only if we do operation of infinity with another type of infinity, then its value changes
Right. While calculating sum of infinite numbers we asume it finite then answer will also tend towards finite number. Hence we start the solution with mistakes.
Sir, You have chosen only one infinite series in your method and you did subtraction operation on the same infinite series that means you are subtracting infinity from infinity virtually which will give indeterminate value
Where as Ramanujan sir had chosen three different infinite series such that when he did subtraction operation on two infinite series he got a different infinite series so in his case there is no indeterminate kind of thing. 🙏🙏
Yes ramanujan sir chose series a
Series b
And series s
U r totally wrong i guess , ramanujan in his first series also subtracted from infinity to infinity A=1-A , so he got the indeterminate value in his first series only , so how can he subtract it in 2nd and 3 rd series . Also in his series A he took 1-1+1-1+1-1+1....infinity , so infinity will end with either -1 or 1 , if -1 then sum of that series is zero , and if 1 then sum of series = 1, only two options . so-1/2 is not valid .
yes
Ramanujan did the same thing subtracting infinite from infinite, even thrice. Look at that proof wisely again sir
Infinity minus infinity is zero or infinity??
-1/8 is correct in 2nd dimension
And
-1/12 is correct in 3rd dimension
And higher dimension
Results must go on like
-1/16
-1/20
-1/24
But point to be notice factor moves manually not exponentially and common factor is 1/4
So results is visual univers or visual concepts is only 1/4
We don't able to see entire universe
Because entire universe or creature of entire universe or infinity visualization is impossible because we don't have a special devine eye
Bro I wanna know why do you said -1/8 is correct in other dimensions
4th dimension is time after that nothing can go further
@@TheGreatestHumour did u ever heard about string theory ( about 11 dimensions)
@@TheGreatestHumourthere are 11 dimensions.
The 4th dimension is time and the 5th dimension is the parallel world, and we can go further
@@noone.4981 well everybody knows that but we can't touch the 5th dimension they are the one who controls tims
I am posting a separate video to disprove Rananujan's theorem, i.e. 1+2+3+..... = -1/12. (separate video to disprove Rananujan's theorem, i.e. 1+2+3+..... = -1/12. : ua-cam.com/video/CWFV43BHsNU/v-deo.html). But your method involves clubbing of 3 or 5 terms in the series infinite times to get the result to be -1/8. Your method implies that the bracketing of 3 or 5 terms will continue exactly as it is till infinity, So, you are softly assuming that infinity is a multiple of 3, 5 etc., which is wrong. In general, infinite terms cannot be bracketed with finite terms in each bracket. That is the problem....
Nice thinking
Great man
You are right brother 👍
Appropriate thought..
रामानुजन sir is correct.
@@satyakumarjnve.champaran4190 no one is correct indian are known for wasting their as well as other time , I lost my day on this topic my exam is 3 days later how can you get negative number when you add tpositive number it is useless not the genius , tell me its uses infinite plus anything is infinite how can you considered this time wasting man as genius just because he is my your nation , look Newtons how useful and logical are his theory and mathmatical operation although there are some limitation even on his theory but really Ramanujan I don't known literally about indians you guys are amazing
finally 😂😂😂😂 your knows infinity yaa😂😂
1+2+3+... = -1/12
This equation can also be proved by euler-reimann zeta function. Can you prove your equation with this method?
We can proove but we must get out of the domain of the zeta function
Do you think Ramanujam didn't calculate -1/8, i don't think because his mind was much sharper than yours and mine. He was the best mathematician of all time. He gave most feasible answer -1/12 i think so. You all are fool. Just reach the level of Ramanujan maths solving approach and define something. People are not able to solve his many equations where he wrote question and answer but not provided any explanation.
Summation of this series can be proved by mock theta function
This is some other way of summing that gives -1/8. It is not surprising because these kind of sums such as cessaro or riemanian are not literal summation. But when you derive something you should start from fundamentals. When you start with grande series you will arrive at -1/12. Rieman zeta function through analytical continuation yields -1/12 as well. So -1/8 is some other kind of sum.
and there exists another analytical function which continuation will give -1/8
You cannot close infinite into bracket because the last term can give any value
Yeah, that's a good thought. You really gave a great reason. Appreciate 🎉👏
But ramanurjan sir also close in bracket and put equal to constant
@@krishanhatria1657 ha
Therefore called it Ramanujan Paradox.
Different mathod to ,you have different answers.
Ramanujan is always right.
But how can we add the series.
@Pooshan HalderChess the solution he is telling in the video is incorrect, as he took triplets upto infinity which can't be taken because it can't be known what will be at infinity.
@Pooshan HalderChess no there is no possibility because, there is no limit.
@Pooshan HalderChess nope. You can't say 2+2+2+2...... = 1++3+5+7......
I'm just trying to say, that nothing can be said, when it comes to infinity, just because we don't know it
Sir as we know that -1/12 is used in many theories because its giving very accurate answer that's why we think that this answer is more correct .is -1/8 also use in any theory of physics?
Can u please name theory where this infinity series is used and has give accurate results ??
@@srinivasramanujan6464 is n(n+1)/2 and -1/12 different things ??
What kind of authoritarian argument is that? Is -1/12 some kind of dogma? Maybe -1/8 is not correct either, but then the whole method is wrong. In a mathematical calculation, when dividing, you must always assume that the divisor is not zero. It is conceivable that in the derivation above, one must also assume that S cannot be infinite. In this case, neither -1/12 nor -1/8 is correct. Apologies if the program has not translated the Hungarian text correctly. It's not dogma that everyone should communicate in this hateful English language.
@@srinivasramanujan6464 it is still a theory brother. First of all we must understand what is a theory. There is difference between truth and theory.
Kya aapke paas koi proof hai koi website ka link vagera bhej do bhai jisme is chiz ka proof ho ki addition of infinity ka use physics me diya gya ho aur accurate value de rya ho
In many instances, people see the video below regarding this Numberphile video and tell me that 1+2+3...=-1/12 is debunked by mathematicians. I left the comment below; please read my comment on the video below, before making any inquiries and assertions.
ua-cam.com/video/YuIIjLr6vUA/v-deo.html
In Mathologer video, I observe three distinct parts:
Firstly, Mathologer demonstrates a lack of understanding regarding the meaning of 1+2+3+...=-1/12 and attempts to use the limit definition and a high schooler's method for divergent series. Consequently, everything presented in Numberphile is deemed incorrect.
Secondly, Mathologer returns to continue the video and realizes that 1-1+1-1...=1/2 makes sense, but the assertion that 1+2+3+...=-1/12 is definitely incorrect.
Lastly, it is delightful to witness Mathologer discovering the actual method behind the true meaning of 1+2+3+...=-1/12, which is Ramanujan's method. However, he neglects to revisit his initial argument from the first day. It is unfair to a genius like Ramanujan to not be appreciated, and the mockery of his work is truly disheartening.
I must acknowledge that Mathologer demonstrates exceptional genius throughout this video. He acquires knowledge that typically takes people much longer to grasp.
Here you can see several proofs for 1+2+3… = -1/12 . ua-cam.com/channels/Bm0bVo59PQgGUCcuWXyHfA.html
Ignoring the Identity Theorem is not a good method. It is interesting that even after so many years, Ramanujan is still greatly misunderstood. Numberphile presents Ramanujan's work, and it is unfortunate that some individuals, have formed a mathematical 'religion' and have disregarded figures like Ramanujan, assuming their own mathematical beliefs as infallible truths. Treating a mathematical concept as a rigid doctrine akin to the Bible, which must be strictly followed, is not helpful. Mathematics is not just a collection of theorems; it is a set of rules that we define and occasionally modify.
For a long time, we have known that the limit definition is poorly defined. Let's consider the series 1-1+1-1... as a switch that we can turn on and off repeatedly. If we do it long enough, we will perceive a light with half intensity. Similarly, in our homes, we have alternating current (AC) power, but we don't observe divergent light. This debunking is comparable to someone claiming that complex analysis is wrong because the square root of -1 does not exist. While that statement may have some meaning, it is completely incorrect. We utilize complex numbers because they are extremely useful. Therefore, constructing arguments based on the poorly defined limit definition is not correct. The limit definition itself has its limitations, just like real numbers, and we need to employ logical reasoning to extend them beyond their obvious range.
Overall, it is highly recommended for everyone to watch this video completely. If viewers possess the same level of intelligence as Mathologer, they will undoubtedly comprehend the true meaning behind the equation 1+2+3...=-1/12.
Actually, I developed another sequence in which the answer is not (-1/8). However, (-1/12) is still valid. I found another interesting method in which I proved that -1/12 is actually correct. Not only this, I proved the other series as well and there is a bit of co-relationship between them. Soon I will try to publish my research. Does anyone knows any forum or department where I can present and publish my work ?
You can publish in UA-cam comments
@@sidcan5979 😂😂
You can publish in any mathematics journal
😂😂🤣😂🤣
But this method is also not wrong!!
Just one question,
How can you say that the things will be in triplets and Quadruplets up to infinity ?
As ramanujan has taken doublet series
Alright, Ramanujan had not divided any series in his proof as sum of " infinite partial sum to some terms".
Making it doublets or quadruplets.
But, The proof by Ramanujan and what shown in this video both are wrong.
See:
ua-cam.com/video/YuIIjLr6vUA/v-deo.html
@@mathsman5219 you are absolutely right . I have also raised voice for same question. And because of no any such type of assumption ramanujan paradox makes its point more clear in comparison to other similar paradoxes....
@@shyamaldevdarshan
Yup,
I would recommend you to watch this video also
ua-cam.com/video/0Oazb7IWzbA/v-deo.html
@@shyamaldevdarshan This is wrong anyway let suppose i have cricket balls which quantity is infinite and there is a big room bigger than this world i put balls in the room like 1 plus 2 plus 3 i continuesly adding the balls in the room like plusing the all natural number in format of balls how it will come to negative challenge to the mathematician
Sum of n +ve integers is n(n+1) /2 lim n tend to infinity will provide infinity. so the answer can be infinity. now we have three possible answers -1/12, -1/8, infinity
Assuming this summation as a constant is like dividing by zero which don't have a definite vale.
Come on guys, it's a paradox. Don't waste your time proving this wrong, that will not make you any genius.
Sir ramanujan was a great mathematician..His theorems and paradoxes are still guiding higher mathematics,,think thousand times before judge the theroms of such extraordinary personality..💙💙🙏🙏radhe radhe
So U r saying that theorems cannot be challenged?
Ur just destroying the fundamental core of maths and science
In maths and science there is no authority anyone can challenge anyone
I am not saying so. But before challenging we should know about our potential and should check whether our claim is to the point or not.
And i think in this case this method claim is absolutely wrong. And the thumbnail is not suitable.👍👍Radhe radhe🙏🙏💙💙💙
@@alice_in_wonderland42 Sum of all Natural numbers = -1/12 is not Theorem. It is Paradox. You should read first different between Theorem and Paradox. 🙂 It is used in String Theory, Gravitational Field Theory and Black Hole radiation is experimental proved with this Paradox and many more theories are used this Ramanujan Paradox. According to Upanisad , half knowledge is more harmful than zero knowledge.
@@7Sujoy you are right .
People have to think over it .
And this is also implies to all youtubers before creating thumbnail.**what say!!😊😊
Ramanujan was talking bullshit about this particular thing
The statement \( 1 + 2 + 3 + 4 + \cdots = -\frac{1}{12} \) is actually an example of a result from a branch of mathematics known as analytic continuation and regularization, rather than a literal sum of an infinite series. Here's a brief explanation:
1. **Divergent Series**: The series \( 1 + 2 + 3 + 4 + \cdots \) is divergent, meaning it grows without bound and does not sum to a finite number in the traditional sense.
2. **Zeta Function Regularization**: The result \( -\frac{1}{12} \) comes from a method called zeta function regularization. The Riemann zeta function \( \zeta(s) \) is defined for \( s > 1 \) by the series \( \zeta(s) = 1 + \frac{1}{2^s} + \frac{1}{3^s} + \cdots \). It can be analytically continued to other values of \( s \), including \( s = -1 \), where it evaluates to \( \zeta(-1) = -\frac{1}{12} \).
3. **Connection to Series**: The connection to the series \( 1 + 2 + 3 + 4 + \cdots \) comes from the fact that this series can be related to \( \zeta(s) \) via analytic continuation. Specifically, if you use the analytic continuation of the zeta function, you can show that \( \zeta(-1) = -\frac{1}{12} \).
So, while the series \( 1 + 2 + 3 + 4 + \cdots \) diverges in the usual sense, its value can be assigned \( -\frac{1}{12} \) through these advanced techniques in mathematical analysis.
Exactly 💯💯
Sir ramanujan ka theorem bilkul sahi hai apne jos tarike se kiye hai wo galat hai aur mai isko galat sabit kar sakta hoon isi theorem ko maine thoda change karke maine kiya hai aur mera answer -1/9 aa raha hai aur apka -1/8 aa raha hai jo ki dono hi galat hai isliye srinivasa ramanujan ka theorem hi sahi unhone uska ek proof diya hai
You are right all natural number is equal to -1/12 not a -1/8
Bhai proof de skte ho kha galat h mere hisab se to yeh reason h enhone no. Of term change kiye h diring the process
Haa
Proof dedo bhai
Ramanujam ka baap hai!
Ramanujan ko galat batana matlab Suraj ko diya dikhana…..
Sir in ramanujan method we know that the infinity is 1 or -1, so he is right
Terms cannot be grouped because you dont know whats the last term is🧐🤔
This is a famous example where one could end up having a wrong answer by simply adding a series. As it can be seen this series is a divergent series and hence one cannot assign a meaningful limit to this series. However , it turns out in the theory of analytic number theory this series is nothing but a Riemann Zeta function evaluated at -1 which has a value of -1/12. Since Zeta function is analytic continuation of the real valued Zeta functions, this series makes sense and the value is mapped to -1/12. Being divergent series , you cannot add it simply by adding the terms. This is one of the many examples of divergent series being misleading at first glance.
In theoretical physics, this sum is used in the evaluation of Casimir force as far as I know. I have heard it's application in the regularisation problem in string theory but I didn't have the privilege to go through the detailed mathematics of string theory yet.
bro your explanations are amazing. please can you tell me where you learn all of this or can you post videos yourself. thank you
It is wrong bcz u can,t comare divergence series with sum finite value=S ...
1:48 error is that you cannot divide infinite terms by 3. First line has infinite terms and the second line has infinite terms divided by 3 and add one more term. This is called Ramanujan Insane Mathematics
He also divide infinite terms bro in his wrong paradox 😂
how can you considered it that no. of terms in an infinite series is factor of 3 , 5 , 7 or 9 it may or may not be divisble in n/(3 or 5 or 7 or 9)
here, you are expecting that ending numbers will perfectly end with a pair of 3 no.s/5 no.s what is the last numbers do no form it? this assumption itself is wrong! that you can fit numbers in group of 3/5 till the very end, there maybe 2/4/ etc. numbers left at end and the answer collapses completely! I am not telling you are wrong, you are partly correct because the sum goes till infinity there are many possible variations to this, you just considered the odd pairs, so -1/8 (ans. for all odd pairs) is just a drop in the ocean of answers, cuz infinity is not defined as incase of 1,2,3 etc. so there are bound to be fallacies, and much interesting anwers!
Bro ramanujan did the same thing.
He proved
1-1+1-1+1-1..........=1/2
Which acc to you is wrong
Do reply if you're seeing this comment.
@@deathmetal4029 I am not telling that it is wrong, it is right (depending on our assumption, to solve the question), because it is the domain of infinity and it is expected that we may find many answers, depending upon the assumption that we have taken, and we have to assume as infinity is not a definite number!
First of all, call him with respect as Sir Ramanujan....
May be you are right but you cannot prove his method as wrong, so don't dare to compare yourself with him
Right
Haati agar baith bhi jaye, to wey gaadhe se bhi uche hotey hain : Rozario, Kolkata.
Yar vo compare thodi kr rah hai khud ko......
You are wrong the answer -1/12
Guys plz dont disrespect anyone of them
Afterall initially toh ramanujan sir bhi ordinary the
-1/12 is used in string theory to understand dimensional analysis so Ramanujan is correct coz its practically proved
Just because something is practical does not make it correct. The Bohr model of the atom is practical but it is not considered correct (true nature of reality). The Bohr model is sometimes more practical than the electron cloud model when it comes to communicating the idea of atoms to high schoolers does that mean it is more correct than the electron cloud model when it comes to high schoolers but more correct outside of high school. Do atoms change how they work whenever somebody models them differently out of practicality? That's absurd. Mathematics does not care first whether something is practical, it cares first whether something is proven logically through the right use of axioms, practicality comes later. Just like how it is practical for humans to see the colours we see through our eyes and not things like xrays, does that mean xrays are not correct because they have been proven to be impractical to see by evolution?
Ramanjuan is correct because he is using a different form of infinite summation. It is defined differently and allows the extension of assigning values to infinite sums which would otherwise be divergent. He is not correct because his work is practical, he is correct because his work logically follows from the way he defined things.
String theory itself is speculative. There is no observation or experiment proof of String theory.
String theory is nonsense it has zero proof and evidence 🤣
String Theory is more Mathematical Pseudoscience than Natural Science.
Thank you for sharing your perspective! Your approach is quite interesting and appears to be a unique way of organizing the series. Let's break it down step by step to explore its implications:
1. Restating Your Argument
You considered the series and grouped terms in a specific pattern:
You identified that certain groups add up to multiples of 9: , , and .
Based on this pattern, you proposed that the sum can be rewritten as:
S = 1 + 9 \times (1 + 2 + 3 + 4 + 5 + 6 + \dots)
2. Algebraic Rearrangement
From your equation, you get:
S = 1 + 9S
8S = -1
S = -\frac{1}{8}
3. Analysis of the Result
The value you derived, , differs from the conventional result of . However, it's important to note that manipulating divergent series like is highly sensitive to the methods used. In standard mathematical frameworks:
The grouping and rearrangement of terms in an infinite series need to be handled carefully because they can lead to different results.
Ramanujan’s original result of is consistent with analytic continuation and the Riemann Zeta function.
Why Does Your Approach Differ?
1. Rearrangement Issue: In the series , rearranging or regrouping terms without a formal method (like analytic continuation) can lead to contradictions because the series is divergent.
2. Conventional Framework: The result comes from analytic continuation, a formal process that extends the domain of functions to assign finite values to divergent series.
3. Your Method: By grouping terms into multiples of 9, you’ve introduced a specific pattern, but such groupings are not generally accepted in formal summation methods.
Conclusion
Your proof highlights the difficulty and non-intuitive nature of dealing with divergent series. It challenges traditional results, showing that divergent series require rigorous frameworks to produce consistent answers. The accepted result of is grounded in methods like the Riemann Zeta function and regularization, which might not align with other groupings or interpretations.
If you have more thoughts or another approach, feel free to share!
Sir actually ramanujan said that sum will be any "negative value " He haven't said it will be always -1/12
Well, for n=1 the sum is 1, i.e. > 0.
A simple proof with en.wikipedia.org/wiki/Mathematical_induction shows that every sum for n>1 must be positive as well.
qed
The author of this video makes the mistake of using S as if it was a finite number, as many commenters have pointed out.
Ramanujan makes a similar mistake of operating with infinite sums (and I believe, different sums over different n's) as if they were real numbers. If the string theory is actually using his proof, then I have some doubt about the string theory.
S- 9S = 1
Par dono S to infinite he
Uska difference nahi kar sakte
infinite - 9(infinite) = 1 😢
9(S) = S hi hoga
Ifinite me kuch b + kro ya - karo wo to infinite hi rahega
Kuch nahi aata maths me tujhe
-1/12 correct hai
Bhai ye duniya infinite ko equation me fit karne ki kosis kar rahi he,, isse unko koi fayda nhi hoga, mene inn sabhi methods ko wrong prove karne ke liye kal hi, teen equation se S ke do maan nikale jo ki different different he. Lekin ab me theoretical kese wrong prove karu, iska solution nikal ne ki kosis kar raha hu.
@@Chesser36 😂😂
@@lalkrishnsolanki -1/12 string theory me use hua hai
Comment on video
Positive number Plus positive number cannot be negative number as per our basic knowledge of algebra.....
But since Ramanujan Sir ( one of the great Mathematician of the world) had given this sum i.e -1/12 ...then there must be reason of it...so this should be discussed worldwide Maths forums.....and should be cleared....all the confusion....
It's like in physics parallel rays of light meet (intersection) at infinity and at that point of intersection image of object is formed when it's placed at Focus point infront of concave mirror, this image is real, inverted and very larger than object...
But in Maths as per present knowledge ....
Parallel lines never intersect each other......
Now what's correct...? Physics or Maths?...
One more point for thinking...
For all these type of confusing questions.. we must think from Very beginning.. without any biaseness...
... So we can conclude totally new approach of solving the problems of any type physics, chemistry, biology, Maths any branch of science.....
Like for the much more times in the Era of Newton it was believed that there's a medium called "eather" between Sun and Earth, through which rays of light passes while reaching on earth, as at that time it was believed that every type of waves need medium to propagate.... ..later on Einstein had proved thet there's no medium like eather between Sun and earth above the atmosphere... sunlight is made-up of electromagnetic waves needing no medium....
The thing is it is based on ASSUMPTIONS that are absolutely wrong. The later infinity is much smaller than the former. Also, idk if the series of taking out 5 or 7 as factor applies as we go further so can't comment on that as I haven't checked for either.
yes ! ramanujam was wrong. we can equate any thing with any thing if we are working with infinte series... First of all 0 and infinite should not be used in mathematical calculations. for eg:
0 = 0
we can also write equation as:
0*5 = 0*4 (because 0 can be written as 0 X 4, or 0 X 5)
lets take 0 as x.
so 5x = 4x
cancelling x on both sides
we get 5=4.
working with infinite also we get things wrong. In infinite series we are condensing the series. so values can expand or contract. we have to take a set of 100 numbers and do that same thing. then the result will be true.
Bhai school mein agar basic maths padhliye hote toh aaj x se x nehi kat te....hope you will understand
@DibakarBiswas-sl6bn you need not teach me basic maths, first learn basic common sense. How come sum of all positive nos be -1/2? You can bring it to Any no. In that case. At 2:53 how come S=1+9S come? Unless it's infinite series. That's what I said. Without knowing the ending of number, It's ridiculous to do calculations with infinite series. if he had taken sum of 4 digits instead of 3 then the result would be different.
Also one thing is if you add exceptions in maths, they come into syllabus. Exceptions are added in syllabus if some calculation goes wrong. I state that calculations on infinitive or infinite series should be termed as as wrong.
I think tha means before finding the sum of infinite number numbers we have to find what infinite really is because ramanujan proof was also mathematicaly correct
How, now modern science has improved, you have to agree that Ramanujan and also the guy on yt is wrong
Sir "Ramanujan" ki proving jayda sahi hai 😀
Kyo
Kyoki infinity ko koi nahi janta 😂😂😂
No one is correct actually you can't bracket any infinite series like ways
Riemann theorem says only absolutely convergent series can be bracketed in different ways but the sum remains unaltered
There is pa branch of mathematics called complex analysis , get look at analytic continuation and whole confusion about this utterly misunderstood Ramanujan formulae will be gone
I think we are simply going against some rule of math which we all including Ramanujan are unaware of. That is why we are getting different answers, like -1/12... -1/8
Because, if we solve properly, then we all should get 1 answer.
In simple terms, sum of all positive numbers will always be positive.
Yes😕😕😔🙄
May be infinite is a number which controls the line of numbers
I think you are a child
@@murtuzamakada3450 infinity is not a number
this doesn't have to be true according to the zeta function. the answer will always be indeterminate
I am fully agree with you. I can't digest Ramanujan method.
Ramanujan ki theory ye thi ki natural number ka sum negative ayega.
Alag alag tarike se alag alag answer ayege but bo sum negetive hi hoga.
So ramanujan and you both are correct. 🙏🙏🙏
I hv proved it to be positive and 1/12
You are wrong sir ramanujan is great mathemathician. he solve tritno mettry in 3-4 line.so he can't mistake in infinity
Sir ramanuzan is a great mathematician and his theories is always right.
Because of fools like you, new mathematicians are unable to emerge in the math domain.
Andhbhakt
@@charmingdawn lol yha kha se andhabhakti aa gyi beech me? He's 100% right. Ramanujan sir just o
proved it
@@ok-hg2in I don't think just proves means it can't be revisited by current mathematicians...
@@jackyjack9660 oh so ur Chinese scientist will prove
I see a lot of potential in you.. just believe in yourself & be more confident
The thing is it's a negative rational number and that too with denominator oscillating between 8 and twelve. Moreover from usual belief the sum should have been infinity. But since logically both answers are correct it can be said that the sum to infinity is an integral of dx with upper limit -1/8 and lower limit -1/12. That's actually a near infinity indeed.
I got the step where he did a mistake. Since infinity is a value that can't be defined, he also cannot say that the sum of (infinity-2)+(infinity-1)+(infinity) is a multiple of 9. He assumed infinity to be a constant whereas it is a variable. The value of Infinity can give any value, so it might not follow the rule he has used to prove that S=-1/8, i.e. taking all the terms as a multiple of 9. I guess that's where it went wrong.
@@noone.4981 Right. I think also that in this series each term should be followed the same action(unlike set of fixed numbers he used in this solution). Then and then only infinite number will also follow it and answer will get finite otherwise answer will be always infinite.
The comment section is filled with blind followers of ramanujan, As a ramanujan admirer, his greates discoveries were the hardy-ramanujan numbers and other series, not the sum of all natural numbers, if you could actually go and study his papers you will discover why he is known as a great mathematician -1/12 is undertiminant and no mathematician would even approve of it. Life dosent end when an obviously divergent series has multiple summations
it can be disproved by the fact that you can only equate the sum to infinity of a series to something if and only if that sum converges . if it doesn't converge it is not equal to something in particular
i think that s = 1+9(s/n) n= times grouped part of s. in your example you ignored that you grouped s to 3 part coefficient of 9 . not convinced
I think the answer -1/12 And -1/8 both are correct. It is Riemann's rearrangement theory.
-1/8 galat hai ans
Yes, esa riemann's rearrangement theory hi define krti ha ki asa kyu ho rha ha
he has prooved this series by even using the 1+1+1+1 thory and supposing it as an variable subsituted to this eq
You are right from your perspective.
And Ramanujan is right from his perspective.
Ramanujan can never be wrong Ramanujan's number paradox is used in higher mathematics and higher physics too so Ramanujan can never be wrong
anybody can be wrong. just takes the right dilemma to disprove it.
@@NITHYASHREEKSPGP-Batch yup it can be I mean he is only human but due to its use in higher mathematics for the current situation I don't think so
When I showed it to ChatGpt the answer came: The series \( S = 1 + 2 + 3 + 4 + 5 + \cdots \) is a divergent series, meaning it does not have a finite sum in the usual sense of convergence. However, in the context of certain mathematical frameworks, such as analytic continuation and the Riemann zeta function, we can assign a finite value to this divergent series.
The argument you provided involves a fallacy in its manipulation. Here is a correct and more rigorous way to understand why mathematicians, including Srinivasa Ramanujan, say that the sum of this series is \(-\frac{1}{12}\):
1. **Riemann Zeta Function:**
The Riemann zeta function \(\zeta(s)\) is defined as:
\[
\zeta(s) = \sum_{n=1}^\infty \frac{1}{n^s}
\]
for \(\Re(s) > 1\). It can be analytically continued to other values of \(s\), except \(s = 1\) where it has a pole.
2. **Zeta Function at \(s = -1\):**
By analytic continuation, the zeta function value at \(s = -1\) is:
\[
\zeta(-1) = -\frac{1}{12}
\]
Hence, we assign the value:
\[
\sum_{n=1}^\infty n = -\frac{1}{12}
\]
This result arises from a more advanced mathematical context and cannot be derived through simple arithmetic manipulations of the series. The series \(1 + 2 + 3 + 4 + \cdots\) is divergent, but in the framework of analytic continuation of the zeta function, it is assigned the value \(-\frac{1}{12}\). This is a well-established result in mathematical physics and string theory, among other fields.
Wow, so, interesting+ amazing for me....Thank you very much, I love this idea.
Whether he is right or wrong it does not matter but he is trying that is encouraging. Einstein show courage to put challenge before Newton.
Sum of Natural Number infinite shall never be Negative. Simple Funda is ( Plus Plus shall always plus) + +=+. Either it is Ramanujan or anybody else. The game is choosing the part and presenting it other way.
Nope did you actually did sum of them that's why you are so sure. Infact no one said that infinite + = + so keep your 2 class maths with you.
@@mathman15Dear Class 2 math is fundamental, that is the thing I am teaching you. Infinate means Infinate you can not count the end. Where there is no end you can not add or subtract the same entity as whole hypothetically. If anything is Infinate it possesses the singularity. Unique + Unique= Unique, and Unique - Unique= 0 it is same for Infinate natural numerals. If there is 1+2+3........=1+2+3.....
Then
1+2+3....-1-2-3...=0
Then
0=0
Ramanujan's case can only be true if we assumed a certain point of end. But infinity doesn't has any end point. ( Copy my theory with permission).
@@ghp780 you have a point but there must be some answer because every math question has a answer if try from different method eventually u you would get -1/12 and the main fact is it is used in string theory which is not wrong so this answer can't can't be wrong. I know that there are some math problem like 5/0 which have no answer but I think there must be some answer and I am working on it.
And my dear friend this ramanujan proved by following all rules of linear equation,Addition,BODMAS , etc so how ramanujan can be wrong and also this is verified by big mathematician also and maths is my favourite subject so I can even verify that ramanujan is correct by his method and I tried other methods also and in those also I got -1/12
Sir ji ye btao sum of all natural number 1+2+3+4+5+6.......=-1/12 negative kyon aa rha 😁😁😁😁.......
Prove this theorem is wrong 😁😁😁😁😁😁😁😁😁😁
There might be a reason for Sri Ramanujan to take different infinite series and put them together to prove the sum! Because it is for SURE that that this pattern had also came in his mind too!!
Can you anyways prove S = -1/12 by your method???
How did you did method for 3 And 5 that means infinity is a multiple of 3 & 5
Hence proved
The answer is -1/12
Sir RAMANUJAN IS PERFECT
You are damn wrong ✖️✖️✖️✖️✖️✖️✖️✖️✖️✖️✖️✖️✖️✖️✖️✖️✖️✖️✖️✖️✖️✖️✖️✖️✖️✖️✖️✖️✖️✖️✖️✖️✖️✖️✖️✖️✖️✖️✖️✖️✖️✖️✖️✖️✖️✖️✖️✖️✖️✖️✖️✖️✖️✖️✖️✖️✖️✖️✖️✖️✖️✖️✖️✖️✖️❌❌❌❌❌❌❌❌❌❌❌❌❌❌❌❌❌❌❌❌❌❌❌❌❌❌❌❌❌❌❌❌❌❌❌❌❌❌❌❌❌❌❌❌❌❌❌❌❌❌❌❌❌❌❌❌❌❌❌❌❌❌❌❌❌
You can group it by that amount of numbers in group how much you have left to be grouped
Sir, in your series you presumed that infinity is odd also that in first series infinity comes after three consecutive nos and also in second series the same holds true but with 5 consecutive nos
सर इसका दोनों आंसर गलत लग रहा है। इसका इस तरह से अनेक आंसर हो सकता है।
जैसे- -1/4, -3/8, -1/2, -5/8,
-3/4, -7/8, -1, -2, -3,...आदि।
सर सभी आंसर गलत लग रहा है।
Sir Ramanujan Srinivasan's calculation is right and what you have shown is wrong. I was also in the same dilemma once as you are in, but I got it right ultimately after 10 minutes of thought.
What you have assumed that the number of elements in the infinite series are in the format of 3n+1 or 5n+2 etc. which is utterly wrong.
Sir Ramanujan's explanation doesn't have any such assumptions.
No one in this world has visualized the infinity the way the great Sir Ramanujan had visualized and we should be very proud of him and the world can't forget his contributions ever.
Saala sahi koi v ho ja na ho but bheje mein toh aapke waala pada -1/12 ko prove krne waalo ka toh kuch samh ni aaya kaise v kuch v assume kar lete hai saale Bina kisi concept k
Ramanujan sir is always right👍👍👍👍👍👍👍👍👍
but sir why you are leaving those numbers?? you can also take them.. DO YOU HAVE ANY EXPLANATION ABOUT THIS?
This great mathematician, not even proved most of his theorems, it just answered out of his intuition and results are perfectly aligned with the facts in nature. He is a devine personality. 🙏🙏
Where muslim
@@candylover6419 Go to quantum level kido.
Infinite must be absolute, it can not be changed. Nothing can be added to it or subtracted from it...
Infinite tak ye 3-3 ke pair ban jayenge is baat ki kya guarantee hai?
Is mamle me Ramanujan ka explanation satik hai.
the invention of Ramanujan was his thought. he was the first who thought the sum of infinite series made of natural numbers could be Negative. In Reality, it’s impossible & it is a paradox.
It is not paradox.the answer he derived is wrong.I have its solution.
What is your solution?@@Connecting-nature
1:38 there should be a + sign after that.
Our Next Ramanuj.
Anyway I appreciate his effort.
👍👍👍👍.
Ramanujan sir's method is correct, your method is worng.
Ramanujan sir use a series
1-1+1-1......=1
1-1+1-1......=0
So average=1/2
We need to average this because we don't know Infinity is odd or even!
But in your method when you sum this
1+(2+3+4)+(5+6+7)+...+(...) That means you consider infinity as odd ,or sometime even so there is ambiguity about infinity is odd or even so your method is totally meaningless.
Basically you saying that you are correct and Ramanujan was wrong!...LOL
I think humans have to discuss more about this . Different mathod gives different types of ans of this question.
Hello I am grade 5 student and I saw this video can anyone tell me what is going on
Jo kisi se nahi hota o ramanujan kadte hai.. Once a king always a king... Of mathematics
Ur wrong I am a small mathematician I did some small researches and proved y
Ur wrong
First of all you have to understand what ramanujan wants to do here. Let we take it as ramanujan wants to prove that sum of natural numbers is divergent. To prove this he uses method of contradiction. He assumes an assumption that let sum of natural numbers is converges to s and in the end he got sum of all natural numbers is negative which is not possible sum of all positive numbers can not be negative . our result is an contradiction so our assumption is fail. Hence he proved that sum of natural numbers isn't convergence series. Actually it is a divergent series.
I think it's an afterthought, more accurately an excuse. The S=-1/12 theorem is a given in physics, more specifically in wave theory.
Bapre ....dimag ki batti jala di😝👍👍👍
-1/12 or -1/8 दोनो भी सही नहीं लग रहे है. मेरे पास इसका answer है. वो भी whole number मे.
-1/12 cause he's a mathemathician genius not u
How do you know?
When we write 1+2+3+4+5+6+7+8+9+10.....infinite ..... You choosen 2+3+4=9and 5+6+7=18....but I will choose 2+3+5=10;14+6=20;7+13+10.....see all terms are in addition we should choose in order is a wrong method.... But ramanajuan.... Found for any series of infinite the answer is -1/12.....dont judge a book by its cover.... He is the backbone to find the black hole concept.... His formula only helped to find about the concept black hole... When he was discovering that black hole formula he don't even know this could brought the end of the concept black hole..... See the history first then speak about him.... HISTORY ALWAYS WINS..... As I took the addition of 10
Therefore I will get.... Let B=1+2+3+4... Infinite
B=1+10(1+2+3+4.... Infinite)
B=1+10B
-9B=1
B=-1/9
Legend never die 😊
Confirm ramanujan was correct.... -1/12 ....
......but many cases -1/8 is also valid 👍
I might be wrong but I think -1/8 is wrong
-you can't be sure that the last number or infinity completes the triplet/quintuplet/septuplate as it can be ended at 1st or 2nd position too.
For eg
Considering last 3 digits and assuming infinity as 11
So the last triplet will be 8-9-10 leaving 11 behind thus proving us wrong
Haha
Sir you have prove S=-1/8 by only one method . The result you drawn first time that is -24S=3. If we multiply the above equation by 2 then we can obtain -48S=6 and by this we can find S=-1/8 by approaching to the soln. in reverse direction.
Hence, there is only one way to prove S=-1/8.🙏🙏
In my opinion we cannot say which is wrong
Because this type of series of is Divergent series. And in their the different types of relations gives different answers.
Only convergent series have a fixed answer
I had been hate math/physics since my childhood, because this one thing I never understood,but I suppose if you whould be my teacher in that time , maybe I would be professor or scientist,but now i'm enjoying to watch Ur video......😃😃😃😃😃😃
Your video is missing the point of Ramanujan summation!
While it's true that you can get any value you like by rearranging the infinite series in different ways, the Ramanujan summation has the property to return the function values of the Dirichlet-eta function and the Riemann-zeta function (though technically the first would be sufficient, since you could use zeta(z) = eta(z) / (1 - 2^(1-z))), which are the unique analytic continuations of the well known series (though they are typically unnamed - but i assume that naming might be helpfull):
eta_series(z) = 1/1^z - 1/2^z + 1/3^z - 1/4^z + ...,
zeta_series(z) = 1/1^z + 1/2^z + 1/3^z + 1/4^z + ...,
eta(z) := Ramanujam Summation of eta_series(z),
zeta(z) := Ramanujam Summation of eta_series(z),
In case eta_series(z) converges, eta(z) = eta_series(z) (same for the zeta).
Those function values are important, because many other functions can be expressed in terms of those, like for example the Jacobian theta-function.
The famous example boils down to:
While the zeta_series diverges at point z = -1, it's function value of the analytic continuations at that point is -1/12.
Or in short:
zeta_series(-1) = 1 + 2 + 3 + 4 + ... = + infinity,
zeta(-1) = -1/12.
Some mathematicians identify the term of the zeta_series at point z with the
unique analytic continuation function at that point, which is the reason that allows them to state that "1/1^z + 1/2^z + 1/3^z + 1/4^z + ... = zeta(z)" (and since the sum diverges, but the term is of course defined and different for any two different value for parameter z, that's only true in that specific sense only!).
The problem in -1/8 is that at infinite it is possible that we can't pair 3 or 5 digit and few digits are left ....
That's why -1/8 is false ....
If you take a number suppose x, then the sum of its predecessor, x and the successor will always be (x-1)+x+(x+1) =3x its always 3x, so clubbing three numbers around multiple of 3 should be always multiple of 3x i.e. 9, why wouldnt it be applicable at infinity, whenever infinity is involved everything just goes senseless, but Sir Ramanujan has understood ot very well still i dont think there's any problem with his explanation tho he should have respected the great mathematician, also i know Sir Ramanujan's conclusion has been used practically in string theory
Right bro there is no logic that why we left some number ...so this is false sir think that he is more genius than ramanujan 😹😹😹
I think the number will tend towards negative but where it will converge is difficult to predict. To visualize this you can try one thing, draw a X/Y number line, keep drawing a straight line for the sum 0+1+2+3+.... until infinity (do not stop). You might notice that for the extremely large number, that line will converge towards Y axis. That means if you still continue, it might fall backward to y-axis, that means tending towards negative side. Thus I think the convergent point ends at (-1/12) => -0.83333333333333............ That means after this point, you do any addition it will be keep moving only at this point.
This is my assumption...
bhai number line me y axis kaha se aa gaya ??? ye complex numbers nahi hai . i know that natural numbers can be represent by complex numbers just by making imaginary part zero but its just the method of representation not the very basic axioms on which math is built.
@@leo_leo_leo_leo_leo366 Bhai think more you will get it..
@@candylover6419 Bhai think more...kuchh bhe ho sakta hai..
@@candylover6419 tu EK baat Bata,
i saal beetne ke baad keya rhega?
@@leo_leo_leo_leo_leo366 y = mx + c is a straight line equation if you know
Bhai wo paradox h 😂
Wow sir .... Maths is mind blowing 🤯🤯
Who first find this.... That sum can be -1/8 also???🤔🤔
Redpenblackpen gives it 1 year ago
Can be zero also...
Ramanujan approach & approach you showed,both are correct.
Maths is filled with imperfections, without assumptions it cannot be done
True
Ramanujan method is right because you use by the method of Riemann paradox it says we arrange series in own way we get result what we want . its depend on arrange meant
Maths is not the perfect language of defining nature , it is just the best language currently avilable to humans for defining nature
Logically, How can the sum of all positive integers be a negetive number ?
But sir your theorem seems more logical as Ramanujan's proof has somewhat not used/ misused Bodmas in the infinity theorem
Great theory sir , you could also have published a research paper on it , so people would more value your work.
Great Counter-video of this theorem sir.
but how can we add things upto the number which does not exist
Sir please reply if you have/ not have published a research paper on it
What is the link of next video?
this video is wrong because he is not continuing the series S=1+9(1+9S) or S=1+9(1+9(1+9S)) or more ... It is infinite. So don't take faulty assumptions . before proving a genius like him wrong check yourself : < l
If we see we are taking infinity as S, and later we are subtracting if from 8S or something, but 8 times infinity if also infinity so it's not defined