Convergent and divergent sequences | Series | AP Calculus BC | Khan Academy

Using the recursive formula of a sequence to find its fifth term. Created by Sal Khan.

AP Calculus BC on Khan Academy: Learn AP Calculus BC - everything from AP Calculus AB plus a few extra goodies, such as Taylor series, to prepare you for the AP Test

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[pbates]

Remember to do your 5 daily prayers brothers and sisters of honors pre calc. We will get through this 🙏

[izzyg.]

You’re doing a great job, but I would be lying if I said watching this didn’t make me actually cry.

[pholoshomothiba]

My very first video from Khan Academy that is just straight forward and understandable. Most of them are long and more confusing. This one is just perfect, mathematically the video converges to "being perfect" as watch time approaces 4:58.

[cameronspalding]

Remember guys if an converges to L:
For all epsylon(eps)>0 there exists +ve integer N such that
n>N implies abs(an-L)<eps
In other words we can get arbitrary close to L

[顾雨-je]

I have been confused by the concept of converge and diverge of series, but this video gives what i want, thank you!

[Ajkikhabar-kf]

A sequence is said to convergent to a no a if for any given €>0, there exist a positive integer n0 such that
|an-a|<€ for all n≥n0

[oneinabillion]

U are the first person to teach me convergence and divergence

[lozzaw]

have you ever wondered what happens if you go from the convergent (0) backwards thus actually expanding per point instead of shirking per point.

[abc]

Can you pls also explain the theorems related in real analysis?

[thesilentvoice]

yeah we can show that for all epsylon >0, there exist +ve integer N such that for all n>N, abs(an -l)<epsilon: |an|<epsilon.

[pinkyjt]

now i get it! that was such a good video! :) thankyou so much!

[nurrohmadi]

what is it mean the limit is not devine to some number. is it mean infinity or the limit just not exist?

[ixiwus]

instead of the power of (n+1), can we use the power of (n-1)?

[misaelrivera]

I dont do calculus but what is the point that math reaches. What can you solve and acheive with advanced math? What are the benefits?

[mannyw_]

Thought he was going to leave me hanging at the end of the video, but there's a followup lol

[dhruvavala]

sir your videos are very helpful.
can you explain me some questions??
*find a function that is continuous at all integer points
*find a function that is continuous at all rational points
*find a function that is differentiable at exact 5 points and
*find a function that is continuous at exact 5 points

[bodozeidler]

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?

[wokguysrandomstuff]

so, the sequence you give as example is convergent right?'

[lozzaw]

so it would be something like,
Lim
n-> - Infinity

provided N belongs to Z number set.

[dzieseliezietsu]

I got 3years to prepare for an And guess what the exam is in 20days and I'm only starting I'm so pathetic...