3:03 may I ask why is it that we're able to insert another equation in between and use that one instead? edit: (my thinking), by an equation larger than the original one, wouldn't its N also be larger? and shouldn't we find the lowest possible N?
i think you typoed at the end, should be ->1,but very clever way of doing this, awesome, thanks for sharing, I don't think I've ever seen it done this particular way:)
Suppose you didn't use the fact that 1/(n+1) < 1/n then you would find n > 1/ε - 1. It will yield the same result at the end. My question is why did you use 1/n > 1/n+1 ? It seems unnecessary. And i am asking this because i have seen this proof in many textbooks done the same way you did it. Am i missing something ?
no you are not, it's just that , I think that n > 1/e is cleaner than n >1/e - 1. You could CERTAINLY do it that way, there is nothing wrong with that, you could say you are ch oosing an integer n such that n > 1/e - 1 via the archimedean property and it's all ok
Why do you have to show every step of your simplifying? Why can't you jump from the definition of convergence to (1/n)? (Trying to save some pencil lead) :D
You explained this very well, and in a fun way! I always get stuck on proofs. Does this show it converges then? And do you have any videos that explain what it means? Thanks!
ya it shows it converges, yeah check my advanced calculus playlist for other convergence proofs, basically it means that when n gets really really big, n/(n + 1) gets really really close to 1:)
so if we let n go to infinity and we get a number, then we say the limit exists, it is the number, in this case 1, and the sequence n/(n + 1) converges to 1
For proving the sequence converges with the formal definition, how would we know when to stop, would be when we reach 1/n in general or varies by each question?
But why is a convergent sum like 1/n regarded as =1, although it never becomes 1 ? Is it by Definition regarded as 1? Or is it a believe that it becomes 1 by Infinite procedure?
Is having the actual value of the limit necessary to be able to prove it's existence? I mean can you prove the existence of the limit _before_ finding it's numerical value?
What would go wrong if I tried to prove that the limit converges to any number other than 1? What would go wrong if I tried to prove that it converges to 2?
At 3:10....How do you know that 1/n is less that epsilon? Since at 4:58 you said we can't just write |(n/n+1)-1| < ε ...please explain this to me....and what does everyone mean when they say they can "choose" epsilon?
because we are figuring it out(it's the scratchwork, so we can do anything), in the proof, the 2nd part, we have to formally show it:) Sometimes people say choose e>0, but really,it's N that we choose. In these proofs we have to find N. I will upload more of these soon. It's a tough topic!!! BTW the reason we can choose N is because of the Archimedean Principle, it says given any number c, we can find a natural number N that is bigger than c. So in this example we chose N > 1/e
Great explanation! One part I got confused on though, why exactly did you need to apply the Archimedean principle and choose an N greater than 1/ε? Couldn't you just keep N = 1/ε, since we're going to end up with the n being greater than 1/ε anyway? Is this because we want N to be a positive integer, and if ε ∉ Z+, we will just have 1/ε ∉ Z+?
So.... I'm new here but.... is no one gonna talk about the rat?
Hahahahahah
Cannot stress how helpful this was ! Been struggling to wrap my head around this, and now it makes so much sense!
awesome!
we need more complicated sequences Amigo..
thanks man, your comment is motivating:)
3:03 may I ask why is it that we're able to insert another equation in between and use that one instead?
edit: (my thinking), by an equation larger than the original one, wouldn't its N also be larger? and shouldn't we find the lowest possible N?
haha my question is how you making this seem simple and interesting...THANK YOU SO MUCH for the help
Thank you❤️
THANK YOU. I've been struggling with this for weeks. I understand it now at last.
awesome!
This guy is saving lives.
nice video ...but i have a confusion...why 1/(n+1)
Because n +1 is bigger than n so the fraction on the left is smaller
Thank you so much! Been so stressed out with online classes! Super helpful!
You are very welcome!
love it when little n is bigger than big n
Sandwich theorem:
Lim(n+1)/(n+1) -> 1 as n -> infinity.
Lim(n-1)/(n+1) -> 1 as n-> infinity.
(n-1)/(n+1) < n/(n+1) < 1
Hence lim n/(n+1) -> infinity as n -> infinity
i think you typoed at the end, should be ->1,but very clever way of doing this, awesome, thanks for sharing, I don't think I've ever seen it done this particular way:)
@@TheMathSorcerer oops yes youre right haha!
Although there's lack of theory, this method of proving and justification is easy to understand!
There's "lack of theory" because the goal in this case is to apply theory to solve a specific case.
about 1.5 yrs later and still a great explanation. Cheers!
👍
This a super solid explanation. Thank you
Thanks so glad it helped
Amazing video! Very understandable
Finally understand this.
Thanks
Thank you, sir. Incredible explanation.
Suppose you didn't use the fact that 1/(n+1) < 1/n then you would find n > 1/ε - 1. It will yield the same result at the end. My question is why did you use 1/n > 1/n+1 ? It seems unnecessary. And i am asking this because i have seen this proof in many textbooks done the same way you did it. Am i missing something ?
no you are not, it's just that , I think that n > 1/e is cleaner than n >1/e - 1. You could CERTAINLY do it that way, there is nothing wrong with that, you could say you are ch oosing an integer n such that n > 1/e - 1 via the archimedean property and it's all ok
I'm reading the mathematical proofs by Gary Chartrand, which is ur prescribed book for proofs,
and I have gone through this problem at 307 th page
Very nice👍
Why do you have to show every step of your simplifying? Why can't you jump from the definition of convergence to (1/n)? (Trying to save some pencil lead) :D
Proving a sequence converges? More like "Phenomenal video with great information for us!"
You've been carrying my mark through university. Thank you for the great vids :)
your explanation is amazing, thanks a ton!!!
You are welcome!
you just saved my life
Would it be the same proof if the denominator is n+2 or n+3?
Very similar yup!!
Im so stressed over mathematical analysis 1 that I'm currently doing 😢,, anyways Thanks alot atleast I'm catching up ,,
thanks i was really strulggling to find the exact wordings to explain that formal defination..iin order to imagine clearly....
👍🏻 easily understandable video👌 ,we want more examples.
I will do more!! thank you!
Good work😃
I might feel something might not logically correct in the scratch work, the statement
(1/n+1)
Great explanation !!!
Thank you !
Cant I say 1/n +1 is less than epsilon? Because when u simplify the original modulus expression it gives u 1/n +1?
I am
writing tomorrow and this was the concept i was confused about until no, Thank you very much.
how were you supposed to know that you had to make 1/n+1
You explained this very well, and in a fun way! I always get stuck on proofs.
Does this show it converges then? And do you have any videos that explain what it means? Thanks!
ya it shows it converges, yeah check my advanced calculus playlist for other convergence proofs, basically it means that when n gets really really big, n/(n + 1) gets really really close to 1:)
so if we let n go to infinity and we get a number, then we say the limit exists, it is the number, in this case 1, and the sequence n/(n + 1) converges to 1
very informative video, thank you
All hail the rat puppet; the only thing carrying me through Calc this year 😩🙏
For proving the sequence converges with the formal definition, how would we know when to stop, would be when we reach 1/n in general or varies by each question?
It was very amazing...I always wondered what is the use of m and then m greater than 1/epsilon....now it's almost clear
❤️
Wow sir👍.
Why is 1/(n+1)
never:) I just used
@@TheMathSorcerer ok, thank you very much
@@TheMathSorcerer I'm actually struggling a bit. I have no idea how to apply the same method for a limit like this:
(-1)^n/(5n-2) = 0
I don't understand why we need n and N, where's the difference ?
You're really a maths wizard fr, thanks for saving my grades.
Why did you switch from 1/n+1 to 1/n ?
Thanks sir
Thank you it helps a lot
great video for explaining the procedure and intuition behind the proof. thanks.
Thanks man
thank you so much. I was stuck with the first exercise. Now I begin to understand how to do it.
Great!
This was the video where it clicked, ty
You are the best !!!
Thx😀
But why is a convergent sum like 1/n regarded as =1, although it never becomes 1 ? Is it by Definition regarded as 1? Or is it a believe that it becomes 1 by Infinite procedure?
Why did you subtract two from the denominator and conclud epsilon is greater than the value .
Thank you very helpful!
Is having the actual value of the limit necessary to be able to prove it's existence? I mean can you prove the existence of the limit _before_ finding it's numerical value?
What would go wrong if I tried to prove that the limit converges to any number other than 1? What would go wrong if I tried to prove that it converges to 2?
sir, how about capital N ??do we just ignore it when we write the final answer? or we can choose both weather ignore or write it?
Kuchh samjh nhi aaya
whether calculus is related to binomial theorm?
you save my life thankyou
You are welcome!
Amazing!
how to show sequences like (1/n,n/(n+1))?
he literally has a video on that. in case some1 else is searching for it here it is:
ua-cam.com/video/B5rqQtp-LIQ/v-deo.html
At 3:10....How do you know that 1/n is less that epsilon? Since at 4:58 you said we can't just write |(n/n+1)-1| < ε ...please explain this to me....and what does everyone mean when they say they can "choose" epsilon?
because we are figuring it out(it's the scratchwork, so we can do anything), in the proof, the 2nd part, we have to formally show it:)
Sometimes people say choose e>0, but really,it's N that we choose. In these proofs we have to find N.
I will upload more of these soon. It's a tough topic!!!
BTW the reason we can choose N is because of the Archimedean Principle, it says given any number c, we can find a natural number N that is bigger than c. So in this example we chose N > 1/e
Very helpful. Thank you
thank you
god sent
This is helpful, thanks a lot!
Awesome!
Nice !
Thank you!
Thank you thank you thank you 🙌🏻
You're so welcome!
Great explanation! One part I got confused on though, why exactly did you need to apply the Archimedean principle and choose an N greater than 1/ε? Couldn't you just keep N = 1/ε, since we're going to end up with the n being greater than 1/ε anyway? Is this because we want N to be a positive integer, and if ε ∉ Z+, we will just have 1/ε ∉ Z+?
right we want N to be a positive integer, that's why