- 102
- 15 186
Praméya Vismáya
India
Приєднався 20 гру 2022
Detailed video lectures in mathematics in Hindi.
*Donation via UPI:* thehiddenlibrary@ibl, zacaffeinemachine@axl
*Telegram Channel:* t.me/thehiddenlibraryofmathematics
Contact me on the following email address: FirstSecondThird@gmail.com where first=za, second=caffeine, third=machine
*Donation via UPI:* thehiddenlibrary@ibl, zacaffeinemachine@axl
*Telegram Channel:* t.me/thehiddenlibraryofmathematics
Contact me on the following email address: FirstSecondThird@gmail.com where first=za, second=caffeine, third=machine
Sequence and Series Lecture 6.1 Series of Powers of Natural Numbers | JEE
*One time donation via UPI:* prameyavismaya@axl
*Full Playlist:* ua-cam.com/play/PLfMiIk4vyppKMhncqBhKBKqiyPMvR4bif.html
*Handwritten Notes:* drive.google.com/drive/folders/1ZOk1-n-vk1UHeMCCr1lWdv3Ij_4fQ7ru
00:00 Recap
00:37 Main Idea
03:53 Sum of Squares of First n Natural Numbers
13:43 Sum of Cubes of First n Natural Numbers
17:14 Illustration 1
18:50 Illustration 2
22:40 Illustration 3
24:55 Illustration 4
30:11 Mains 2019
33:15 Mains 2017
39:44 JEE 2007
44:55 JEE Advanced 2009
49:28 JEE Advanced 2010
54:18 JEE Advanced 2013
01:01:19 JEE Advanced 2022
*Full Disclosure:*
- The general philosophy of my channel is to NOT have multiple versions of the same course.
- I would not be making one-shots, revision-courses, crash-courses etc.
- There will be one definitive and solid course for every chapter.
- The material in the lectures will not necessarily be tailor made to sharpshoot at JEE questions alone. The point is to teach good mathematics and teach it well. This does not mean that your JEE preparation will be compromised. Quite the opposite.
*Practice Problems and other Material:*
- Almost every lecture features practice problems towards the beginning.
- Handwritten notes are linked in the description of every video.
- At some point I would like to send out typed notes will full theory covered.
*As for the PYQs:*
- I would be solving all the JEE Advanced PYQs starting from 2009 onward in my lecture series.
- I would be covering various PYQs from JEE Mains during the lectures and lot of them will be given in the problem sets.
- There will NOT be lecture series solely focused on PYQs. One learns mathematics by doing not by watching.
*Goal of the Channel:*
- I want to make solid courses for each and every chapter relevant to JEE Mathematics.
- After completing math courses I would like to do the same for Physics.
- After that I would like to create material for Olympiads.
- Overall, I want to improve the level of mathematics education in India, and every child should have access to high quality material to learn the same.
#iitjee #jeeadvanced
*Full Playlist:* ua-cam.com/play/PLfMiIk4vyppKMhncqBhKBKqiyPMvR4bif.html
*Handwritten Notes:* drive.google.com/drive/folders/1ZOk1-n-vk1UHeMCCr1lWdv3Ij_4fQ7ru
00:00 Recap
00:37 Main Idea
03:53 Sum of Squares of First n Natural Numbers
13:43 Sum of Cubes of First n Natural Numbers
17:14 Illustration 1
18:50 Illustration 2
22:40 Illustration 3
24:55 Illustration 4
30:11 Mains 2019
33:15 Mains 2017
39:44 JEE 2007
44:55 JEE Advanced 2009
49:28 JEE Advanced 2010
54:18 JEE Advanced 2013
01:01:19 JEE Advanced 2022
*Full Disclosure:*
- The general philosophy of my channel is to NOT have multiple versions of the same course.
- I would not be making one-shots, revision-courses, crash-courses etc.
- There will be one definitive and solid course for every chapter.
- The material in the lectures will not necessarily be tailor made to sharpshoot at JEE questions alone. The point is to teach good mathematics and teach it well. This does not mean that your JEE preparation will be compromised. Quite the opposite.
*Practice Problems and other Material:*
- Almost every lecture features practice problems towards the beginning.
- Handwritten notes are linked in the description of every video.
- At some point I would like to send out typed notes will full theory covered.
*As for the PYQs:*
- I would be solving all the JEE Advanced PYQs starting from 2009 onward in my lecture series.
- I would be covering various PYQs from JEE Mains during the lectures and lot of them will be given in the problem sets.
- There will NOT be lecture series solely focused on PYQs. One learns mathematics by doing not by watching.
*Goal of the Channel:*
- I want to make solid courses for each and every chapter relevant to JEE Mathematics.
- After completing math courses I would like to do the same for Physics.
- After that I would like to create material for Olympiads.
- Overall, I want to improve the level of mathematics education in India, and every child should have access to high quality material to learn the same.
#iitjee #jeeadvanced
Переглядів: 95
Відео
Functions Lecture 9 Bijective Functions | JEE
Переглядів 12316 годин тому
*One time donation via UPI:* prameyavismaya@axl *Full Playlist:* ua-cam.com/play/PLfMiIk4vyppL5JZdxmeRBFpxGpx5VjTcv.html *Handwritten Notes:* drive.google.com/drive/folders/1TgUsEFhYv9HAV1zLsr0ToxAL22DltBK0 00:00 Recap 00:15 Problems 00:21 Bijections 19:05 Inverse of a Bijection 31:32 A Note of Caution 33:28 A Mundane Exercise (Optional for JEE) 43:26 Number of Injective Functions (Optional for...
Sequence and Series Lecture 5.4 Cauchy-Schwarz Inequality (Optional) | JEE
Переглядів 11221 годину тому
*One time donation via UPI:* prameyavismaya@axl *Full Playlist:* ua-cam.com/play/PLfMiIk4vyppKMhncqBhKBKqiyPMvR4bif.html *Handwritten Notes:* drive.google.com/drive/folders/1ZOk1-n-vk1UHeMCCr1lWdv3Ij_4fQ7ru 00:00 Recap 00:40 Problems 00:46 Cauchy-Schwarz Inequality 10:02 Illustration 1 11:34 Illustration 2 14:10 Illustration 3 18:05 Illustration 4 21:38 illustration 5 *Full Disclosure:* - The g...
Functions Lecture 8 Surjective Functions | JEE
Переглядів 91День тому
*One time donation via UPI:* prameyavismaya@axl *Full Playlist:* ua-cam.com/play/PLfMiIk4vyppL5JZdxmeRBFpxGpx5VjTcv.html *Handwritten Notes:* drive.google.com/drive/folders/1TgUsEFhYv9HAV1zLsr0ToxAL22DltBK0 00:00 Recap 00:44 Problems 00:51 Surjective Functions 05:58 An Interesting Fact 09:10 Surjections and Compositions 14:29 A Property of Surjective Functions (Optional for JEE) 20:05 Connectio...
Sequence and Series Lecture 5.3 Multiple Means | JEE
Переглядів 142День тому
*One time donation via UPI:* prameyavismaya@axl *Full Playlist:* ua-cam.com/play/PLfMiIk4vyppKMhncqBhKBKqiyPMvR4bif.html *Handwritten Notes:* drive.google.com/drive/folders/1ZOk1-n-vk1UHeMCCr1lWdv3Ij_4fQ7ru 00:00 Recap 00:41 Problems 00:47 Definitions 02:31 Illustration 1 06:47 Illustration 2 09:25 Illustration 3 *Full Disclosure:* - The general philosophy of my channel is to NOT have multiple ...
Functions Lecture 7 Injective Functions | JEE
Переглядів 14414 днів тому
*One time donation via UPI:* prameyavismaya@axl *Full Playlist:* ua-cam.com/play/PLfMiIk4vyppL5JZdxmeRBFpxGpx5VjTcv.html *Handwritten Notes:* drive.google.com/drive/folders/1TgUsEFhYv9HAV1zLsr0ToxAL22DltBK0 00:00 Recap 02:34 Injective Functions 09:26 An Interesting Fact 15:25 Injections and Compositions 19:41 An Interesting Injection (Options for JEE) 23:02 Recall: Fibers 24:23 Partitions (Opti...
Sequence and Series Lecture 5.2 AM-GM Inequality: General
Переглядів 10214 днів тому
*One time donation via UPI:* prameyavismaya@axl *Full Playlist:* ua-cam.com/play/PLfMiIk4vyppKMhncqBhKBKqiyPMvR4bif.html *Handwritten Notes:* drive.google.com/drive/folders/1ZOk1-n-vk1UHeMCCr1lWdv3Ij_4fQ7ru 00:00 Recap 01:50 Problems 01:55 The Inequality 05:06 Illustrating the Key Idea for the Proof 18:05 A Geometric Preliminary 21:25 QM-AM Inequality for 3 Numbers 25:35 AM-GM Inequality for 3 ...
Functions Lecture 6 Inclusion-Exclusion | JEE
Переглядів 12614 днів тому
*One time donation via UPI:* prameyavismaya@axl *Full Playlist:* ua-cam.com/play/PLfMiIk4vyppL5JZdxmeRBFpxGpx5VjTcv.html *Handwritten Notes:* drive.google.com/drive/folders/1TgUsEFhYv9HAV1zLsr0ToxAL22DltBK0 00:00 Recap 04:06 Illustrating the Key Point 11:09 Inclusion-Exclusion 14:48 Preparation 18:25 Proof of Preparatory Lemma 18:56 Proof of Inclusion-Exclusion *Full Disclosure:* - The general ...
Functions Lecture 5 Real Valued Functions | JEE
Переглядів 10921 день тому
*One time donation via UPI:* prameyavismaya@axl *Full Playlist:* ua-cam.com/play/PLfMiIk4vyppL5JZdxmeRBFpxGpx5VjTcv.html *Handwritten Notes:* drive.google.com/drive/folders/1TgUsEFhYv9HAV1zLsr0ToxAL22DltBK0 00:00 Recap 00:19 Problems 00:25 Real Valued Function 03:17 Sum, Product, Max, Min 10:39 Algebra of Real Valued Functions 13:55 Important Observations *Full Disclosure:* - The general philos...
Sequence and Series Lecture 5.1 AM-GM Inequality for Two Terms | JEE
Переглядів 10921 день тому
*One time donation via UPI:* prameyavismaya@axl *Full Playlist:* ua-cam.com/play/PLfMiIk4vyppKMhncqBhKBKqiyPMvR4bif.html *Handwritten Notes:* drive.google.com/drive/folders/1ZOk1-n-vk1UHeMCCr1lWdv3Ij_4fQ7ru 00:00 Recap 00:33 Problems 00:39 QM-AM-GM-HM of two Numbers 06:38 Geometric Interpretation 09:33 Important Point 18:15 Illustration 1 21:26 Illustration 2 24:06 Illustration 3 29:12 Illustra...
Functions Lecture 4 Cartesian Products | JEE
Переглядів 9821 день тому
*One time donation via UPI:* prameyavismaya@axl *Full Playlist:* ua-cam.com/play/PLfMiIk4vyppL5JZdxmeRBFpxGpx5VjTcv.html *Handwritten Notes:* drive.google.com/drive/folders/1TgUsEFhYv9HAV1zLsr0ToxAL22DltBK0 00:00 Recap 00:21 Problems 00:26 A Motivating Example 01:58 Cartesian Product 11:32 Boolean Hypercube 15:08 A Formal Viewpoint (Optional) 18:44 Universal Property (Optional) *Full Disclosure...
Functions Lecture 3 Composition | JEE
Переглядів 233Місяць тому
*One time donation via UPI:* prameyavismaya@axl *Full Playlist:* ua-cam.com/play/PLfMiIk4vyppL5JZdxmeRBFpxGpx5VjTcv.html *Handwritten Notes:* drive.google.com/drive/folders/1TgUsEFhYv9HAV1zLsr0ToxAL22DltBK0 00:00 Recap 00:33 Problems 00:38 Composition 06:14 Examples 10:01 Properties of Composition 17:34 Another Look of Preimage (Optional for JEE) *Full Disclosure:* - The general philosophy of m...
Functions Lecture 2 Image and Preimage | JEE
Переглядів 137Місяць тому
*One time donation via UPI:* prameyavismaya@axl *Full Playlist:* ua-cam.com/play/PLfMiIk4vyppL5JZdxmeRBFpxGpx5VjTcv.html *Handwritten Notes:* drive.google.com/drive/folders/1TgUsEFhYv9HAV1zLsr0ToxAL22DltBK0 00:00 Recap 04:03 Lecture Overview 04:36 Image 13:03 Image: Union and Intersection 22:00 Image: Set Difference 23:44 Preimage 29:49 Preimage: Union, Intersection, Set Difference 33:47 Fibers...
Functions Lecture 1 Definition | JEE
Переглядів 324Місяць тому
*One time donation via UPI:* prameyavismaya@axl *Full Playlist:* ua-cam.com/play/PLfMiIk4vyppL5JZdxmeRBFpxGpx5VjTcv.html *Handwritten Notes:* drive.google.com/drive/folders/1TgUsEFhYv9HAV1zLsr0ToxAL22DltBK0 00:00 Prerequisites 00:28 Overview 00:56 "Definition" 10:06 Examples 13:13 Numerical Examples 18:01 Non-Examples 20:35 Set of All Maps *Full Disclosure:* - The general philosophy of my chann...
Sets Lecture 8 Size of a Set | JEE
Переглядів 99Місяць тому
*One time donation via UPI:* prameyavismaya@axl *Full Playlist:* ua-cam.com/play/PLfMiIk4vyppIpneJHrYHnaf64RWRw1c0Y.html *Handwritten Notes:* drive.google.com/drive/folders/15HeW7UqKSCqF2xqTkFobvaqAMS5CyWMu *Associativity of Symmetric Difference:* proofwiki.org/wiki/Symmetric_Difference_is_Associative 00:00 Recap 00:28 Problem 00:36 Size of a Set 03:06 Size of the Power Set 09:07 Proper Proof 1...
Sequence and Series Lecture 4.2 AGP: Sum of Infinitely Many Terms
Переглядів 139Місяць тому
Sequence and Series Lecture 4.2 AGP: Sum of Infinitely Many Terms
Sequence and Series Lecture 4.1 Arithmetico-Geometric Progression Sum of Finitely Many Terms
Переглядів 101Місяць тому
Sequence and Series Lecture 4.1 Arithmetico-Geometric Progression Sum of Finitely Many Terms
Sequence and Series Lecture 3.2 Harmonic Progression: Three Terms | JEE
Переглядів 104Місяць тому
Sequence and Series Lecture 3.2 Harmonic Progression: Three Terms | JEE
Sequence and Series Lecture 3.1 Harmonic Progression: Definition | JEE
Переглядів 92Місяць тому
Sequence and Series Lecture 3.1 Harmonic Progression: Definition | JEE
Sequence and Series Lecture 2.7 Sum of Infinite GP: Illustrations | JEE
Переглядів 100Місяць тому
Sequence and Series Lecture 2.7 Sum of Infinite GP: Illustrations | JEE
Sequence and Series Lecture 2.6 Sum of Infinite GP Part 1 - General Formula | JEE
Переглядів 156Місяць тому
Sequence and Series Lecture 2.6 Sum of Infinite GP Part 1 - General Formula | JEE
Sequence and Series Lecture 2.5 Sum of a GP Part 2: Illustrations | JEE
Переглядів 90Місяць тому
Sequence and Series Lecture 2.5 Sum of a GP Part 2: Illustrations | JEE
Sequence and Series Lecture 2.4 Sum of a GP Part 1: General Formula | JEE
Переглядів 872 місяці тому
Sequence and Series Lecture 2.4 Sum of a GP Part 1: General Formula | JEE
Sets Lecture 6 Union and Intersection | JEE
Переглядів 872 місяці тому
Sets Lecture 6 Union and Intersection | JEE
Binomial Theorem Lecture 4.5 Coefficient Method for Hypergeometric Series | JEE
Переглядів 1402 місяці тому
Binomial Theorem Lecture 4.5 Coefficient Method for Hypergeometric Series | JEE
Sequence and Series Lecture 2.3 Geometric Progression: Three Terms in GP | JEE
Переглядів 1462 місяці тому
Sequence and Series Lecture 2.3 Geometric Progression: Three Terms in GP | JEE
Sequence and Series Lecture 2.2 Geometric Progression: General Term | Hindi | JEE
Переглядів 692 місяці тому
Sequence and Series Lecture 2.2 Geometric Progression: General Term | Hindi | JEE
Sequence and Series Lecture 2.1 Geometric Progression: Introduction | Hindi | JEE
Переглядів 702 місяці тому
Sequence and Series Lecture 2.1 Geometric Progression: Introduction | Hindi | JEE
Sequence and Series Lecture 1.5 Arithmetic Progression A Fact About Division | JEE | Hindi
Переглядів 842 місяці тому
Sequence and Series Lecture 1.5 Arithmetic Progression A Fact About Division | JEE | Hindi
sir do u have any group?
The link to a telegram groups is on the Home tab.
Are you missing @sonoftesla in group 😅
The group is pretty silent indeed.
Sir 2- 3 din me khatam kardijiye please sir🙏🙏🙏
2-3 din mein nahi ho payega. 4 lecture aur hain. 10 din mein ho jana chahiye,
how many are here just 20 days before jee !!😅
Bring one for coordinate
Next is straight lines.
Goated
wow sir
Geometrical interpretation of am gm hm was just wonderful❤
Thank you sir ❤
Bhaiya next lecture pnc ka kardo
Next series pls of pnc
I would be doing straight lines next. Can't say when I can start PnC.
Sir please sequence and series complete kardo jee mains january attempt ke phele. Please sir my sequence and series chepter is very weak. Muche app ke video deker concept clear hoja ta hai. Issi liye sir please complete karado this chapter for quick. Please 🙏
About 5 more lectures to go. Main ke pehle ho jana chahiye.
Thank you sir ❤
Sir please also start fom (inequalities, modulus, logarithm) + quadratic equations and polynomial from basic to advanced Olympiad level
My plan is to cover all topics before JEE 2026. But I can't make promises.
Please also cover the other inequalities used in sequence and series chapter for advance questions...
Can you tell me the names of the inequalities that you would like to be covered? Also, I did not find JEE Advanced questions around inequalities. Let me know if I missed those questions?
Oh wow unexpected
Thanks a lot! Excellent lecture as always and the thumbnail change is more pleasing to the eye. Not that the previous ones weren't good but these ones are more appeasing.
Please start a problem solving series for olympiad maths where u can take NT, combinatorics, and geometry problems its gonna be fun. Like some RMO, USAMO, INMO problems. BTW Ur videos are actually so good
We would be having live online discussions with ISI/CMI and Olympiad problems in mind starting Feb 2025. If you are interested then you can join the corresponding Telegram group whose link you can find in the 'About' of the channel.
Will you cover relations in this chapter or as seperate chapter? And When? If yes then also add equivalence classes to it as it is given in NCERT. Thanks
I would make a separate playlist for relations but as of now I do not know when.
Sir 3D geometry and vector complete karo for jee 2025 january attempt
sir how many more video on function?
2 more.
How many lectures left to complete this lesson
About 6 more lectures.
@prameya_vismaya ok sir
You gained a sub, nice explanation. I just want to ask when will other portions of maths start, like Probability and Calculus.
I would like to finish all the JEE topics by JEE Advanced 2026 (though I can't make promises). The more people watch the faster I can make these. Also, I can't say when exactly I would be covering the two topics you have mentioned. I would be doing quadratic equation and straight lines next.
Amazing sir as always
Thanks a lot! Hats off to your dedication to both the channels.
sir are you into samskrita as youre channel name contains the word from samskrit glossary
I am into Hindi. This channel helps me learn a little bit.
sir may i ask u when u will start trigonometry i am eagerly waiting for it!!!!!!!!!!!!!
That is unclear. The next topic is going to be straight lines. After that I think I would do Quadratic Equations. Trigonometry can be taken after that.
@@prameya_vismaya ok sir
sir may i ask you when you will start trignoemetry
That is unclear. The next topic is going to be straight lines. After that I think I would do Quadratic Equations. Trigonometry can be taken after that.
Dammn mera youtube algorithm crazzy work kr raha hun, aapki explanation bohat achhi hai thank you so much..
He has this second bigger channel, "The Hidden Library of Mathematics". Search it, i's awesome.
And for physics search "Sridhar Reddy Physics", you won't be disappointed.
can u make a lecture on counting functions its a very tricky topic
Can you elaborate on what you mean by "counting functions"?
@prameya_vismaya Number of onto functions number of into functions woh pnc wale questions type
I will be covering that in Lecture 9.
sir is sequence and series completed ??
About 7 more lectures to go.
I didn't get the method of forming the graph of the infinite series, do we have to make sure that the base is 1 (which is equal to the first term) but what about the slope? do we also need to make sure it equals the first term or something like that? Do we need to make the second equation in the form y=rx where r is the common ratio? *Sir I am confused what is the general method we are using to make the graph? *What things we need to keep in mind while making the graph? *Also isn't the r in Toy Problem 3 is -2? If yes then how will it affect the graph? *Any particular book where I can find this method to solve the infinite GP sum series in detail?
Is the construction in the Toy Problem 1 clear? If yes, then you should first try to figure out the corresponding construction for 1 + 1/r + 1/r^2 + ... If not then let me know. Yes, in the Toy Problem 3 the common ratio is -2. I said that it is 2 but that was a slip of tongue. The discussion is undisturbed. There is a book "Proof Without Words" by Roger Nelson where a plethora of geometric proofs are given for a myriad of algebraic identities. This approach for an infinite GP (which is folklore) should certainly be present there.
dang goldmine
Thanks a lot, it was an awesome lecture. And really appreciate it that you took such long lectures. Thanks a lot.
Note. The audio in this lecture is subpar. I recorded this on a bad throat. Future ones will have better audio.
the drive link is improperly formatted
Thank you for letting me know. This will take a lot of time to fix :(
You're amazing! Keep going I love your videos ❤❤❤
sir i am watching youre lectures for a very long time now can you please announce a course for jee 2026 so that i can join pls sir
These videos on UA-cam are meant for JEE Preparation. There is no point to a separate course. We will have live discussions after JEE 2025. But those will be discussions. Not lectures.
@@prameya_vismaya ok sir
@@prameya_vismaya but i can do one on one teaching with you ? as i often get distracted when studying from youtube i only want 2-3 classes per week nothing much as i am flabbergasted by your teaching
I have provided handwritten notes in the description of the videos. You can try those if you get distracted when watching the videos. I have hardly any time for private classes.
@@prameya_vismaya ok sir no problem your'e yt content is also way too good
At 21:53, you had assumed that denominator was not negative when you multiply denominator on both side of the inequality and kept the inequality unchanged. How? I used triangle inequality to prove that. By squaring and rearranging terms. Is there a simple reason that I did not see why denominator is positive ? Edit. Simpler proof, 0<= |z -w|^2 = (z -w)(z - w)"bar" = (z-w)(z"bar" - w "bar") .. now opening it we get the denominator
You are right that I should have mentioned that that the denominator is positive. But as you have noticed in your comment that the denominator is nothing but the square of |z - w|.
Thank you sir!
Hey dear, if you re a neet or jee student then comment me.. I will give me notes of every chapter for free and get your doubt solve at free of cost and I will also give you many mock tests to boost up your preperation...
Sir there is a confusion that whether I should share your channel to my friends and competitors who are really preparing for jee advanced coz concepts and teachings are lot awesome but comes in mind about the increase in competition 😅
Jitne zyada log dekhenge utni jaldi main complete kar paunga. Aur phir iske baad Olympiads and Physics bhi hai.
Share it only genuinely interested people will follow. Rest who are not gonna study, they won't either way.
Sir a request can we just do like one chapter at a time, like all videos on 1 chapter then next chapter ,it will help a lot, otherwise it feels scattered
I am doing my best. It may feel scattered now but these videos are supposed to be made only once (with successive refinements if needed). So even if it feels scattered now, once a playlist is finished then it is there to be followed in a sequence. By the end of next year or two I plan to cover all chapters in full detail.
Sir In illustration 3, in the problem you have mentioned that a1>0 but the answer was -12. Is there a mistake or am I missing something?
Good catch. The question should say a_1 < 0, a_2 > 0, a_3 < 0, a_4 > 0. Thanks for the correction.
thank you sir loved this lecture!!!! in last question i solved by expanding , bringing everything to LHS and then multiplying by 2 and then 3 whole squares formed then x^2>=0 so x=0 case and ultimately landed there :)
Yes that is another way to do it. Your point is x^2 + y^2 + z^2 - xy - yz - zx = [(x - y)^2 + (y - z)^2 + (z - x)^2]/2 and this is another way of showing that x^2 + y^2 + z^2 >= xy + yz + zx with equality holding only when x = y = z. At the heart of it this is the same as what we did in the video. But good job!
@@prameya_vismaya yes sir in end you commented ki "abhi am gm padha toh ye striked , so i tried without thinking about am gm , its somehow fascinating like all the way leads upto one Truth
@@anaamikaaa My point was that you can see the connection between the two different ways quite clearly. To prove x^2 + y^2 + z^2 >= xy + yz + zx, we said using AM-GM that x^2 + y^2 >= 2xy, y^2 + z^2 >= 2yz, z^2 + x^2 >= 2zx and then added the inequalities. But these inequalities are saying nothing but that (x - y)^2 >= 0, (y - z)^2 >= 0, (z - x)^2 >=0 (and this is how we proved AM-GM for 2 numbers). So even though your approach is slightly different from the one I have used in the video, they are minor variations of each other.
@@the_hidden_library yes you are right sir