Convergent sequences are bounded

Convergent Sequences are Bounded

In this video, I show that if a sequence is convergent, then it must be bounded, that is some part of it doesn't go to infinity. This is an important result that is used over and over again in analysis. Enjoy!

Other examples of limits can be seen in the playlist below.

[Kdd]

In 3-4 years time he will become as intelligent as Ramanujan or Carl Friedrich Gauss and so he will do a lot of research and he will become famous all over the world and his channel would have been subscribed by (10 tetrated 10 times) no. of subscribers. Best of luck dr Peyam!!! He is a mathematical legend:)))) love from India

[roche]

This is the only video about this topic that I've managed to understand. Pictures are crucial to my understanding of real analysis, and you made it crystal clear in this video. Thanks Dr Peyam!! 😍

[felipeandregp]

Thank you so much!!! greetings from Brazil

[sarojpandeya]

😍😍😍 i was searching this part of real analysis. Thank you

[cloudhuang]

Excuse me sir, isn't there any posibility that a convergent sequence thought converges eventually but "blows up" to infinity for some of the first "N terms" so that makes the sequence unbounded?

[AubreyForever]

If a convergent sequence converges (I think it means has a limit) why do you have to prove it is bounded? I am in grade school and this doesn't make sense.

[godinhos]

Dr peyan, thanks so much to show that intersting math, but i need to help about geometry calculus, like a tensors and your rules of doc and cross product and derivatives of this, it's helps all peoples to undersatand the Einstein's G.R and i in my field theory, i'm a electrical engineering student and i like to physics and if you try to make one series about tensor and geometry calculus i'm so gratefull 👏👏 Thanks dr pyman, and i go to subscribe

[pesilaratnayake]

Hi Dr Peyam. I liked the video, but I was wondering how this compared to functions that converge as x approaches infinity. For example f(x)=1/(x^2-4) which approach 0 as x approaches infinity but blows up as x approaches 2. If Sn=1/(n^2-4) it doesn't have limiting behaviour at 2 but is undefined. Is this no longer a sequence because it is not defined at 2, or is it treated as bounded because there is no limiting behaviour at 2? Thanks :)

[hatdog]

Hey dr peyam.. can i ask if there is a general rule in finding the laplace transform of functions in the form of (t^p)(sinkt) where p is a fractional exponent, say 1/2, 1/4, etc.. this would be a challenge problem for you sir..

Im vincent esperanza from philippines :p

[dr.peyamsfan]

I don't really think u need to write max(abs(S1), u can just write that without abs because u have drawn it in the first quadrant. But, Still this is important coz u didn't say that the sequence is located only in the first quadrant lolll