Does the sequence converge or diverge? (KristaKingMath)

Learn how to determine whether the sequence converges or diverges. In this problem I show you how to find the limit of the sequence, if it exists, and then use the existence or nonexistence of the limit to draw a conclusion about the convergence of the sequence. Alternately, I show you how to use Squeeze Theorem to first draw a conclusion about the convergence of the sequence, and then to use the result to find the limit of the sequence, if it converges.

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Hi, I’m Krista! I make math courses to keep you from banging your head against the wall. ;)

Math class was always so frustrating for me. I’d go to a class, spend hours on homework, and three days later have an “Ah-ha!” moment about how the problems worked that could have slashed my homework time in half. I’d think, “WHY didn’t my teacher just tell me this in the first place?!”

[billwindsor]

Krista King is one of *the best* AP Calculus instructors on the Internet.

[TheDarkProdigy]

You have been a big help on my trimester for Calculus 2, i have been all over the place trying to find videos that can help me understand this difficult subject. Thanks for this videos!

[genta]

when a youtube video is easier to understand then ur paid professor XD

[Primitive_Code]

Now I see why my textbook is barking so much about squeeze theorem early on. Great video. You should be a calc teacher.

[cmdrbobert]

This video really helped me gain some intuition around convergence and divergence, thanks

[imanhosseini]

Thanks teacher King, that rephrasing of the questions at the beginning of ur vid was GREAT!!!

[justinclark]

I'm trying to find convergence or divergence of
∑n=1 to ∞ of cos(log(n))/n
I've tried to use the squeeze theorem, but my professor said it doesn't work for series just like you said. can you help?

[tonAlts]

I was having a difficult time understanding this topic, I went to youtube and found this tutorial. I hope I pass the exam today :) a great help thanks!!

[jordanrobinson]

I've been watching your videos ever since I started Cal 1. Thank you so much for taking the time to make them!

[CamoflaugeCamellia]

Thank you so much for this problem!! This was actually on my calculus II exam. You are so great and have helped through my past classes. Thank you so

[coloredpandas]

I watched another great video like this one but they didn't explain the squeeze theorem so I was lost so I'm grateful I came across yours and understood your explanation... Thankyou!!!

[lorib]

thank you so much, I've been going to several of your videos to help my son through an online Calc class! So awesome to have some female voices out there for math to supplement some of the great guys out there too. Keep up the good work! - Mom the engineer

[itsiwhatitsi]

With your voice even math can be sweet!

[sagunshakya]

And the simplest explanation.. I think it was pretty awesome. Thank you for it.

[APh_]

How do I do this if I am given a sequence without the function that generates the sequence (it is given that the sequence isn't an arbitrary sequence)?

[sheikhs.mahmud]

Do you happen to have a video where you do limits of any sequences that you need to use squeeze theorem to find the limit and determine its convergence or divergence? There was a homework problem which was : lim n approaches infinity of sin n / n and while I know that it is 0 and it converges, I want to know if it is possible to use squeeze theorem? Also, do you happen to make videos for finding recursion formulas for any terms given and finding nth term? If so, let me know. Thanks :)

[seanwalton]

Does the limit [1, infinity) of sum(1/n) converge? Empirically it doesn't. Is that correct? How would one prove it?

[Bytme]

What an incredibly helpful video. It was very clear and you even covered sandwich theorem.

[jared]

You made the squeeze theorem easy af. I was taught it another way a little more complex, hopefully this will work on my test :)

[Mughrabi]

i've been told that limt when n-->infinty for a sequence = 0 does not imply convergent so is there another way to know that ?