Alternating Series, Types of Convergence, and the Ratio Test

An alternating series is one in which the terms alternate sign, so positive, then negative, then positive, etc. How can we generate a series like this, and how can we find out whether it is convergent or divergent? Find out now!

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[cpersn]

Kinda funny how you explain concepts better in 12 minutes than multiple hours of lecture from my professor.

[brysonmutinda]

Simply the BEST proffesor, you make difficult things simple

[rirhassan]

just to let u know ..u explain much better than my uni professor ....u r so good understood all of it in 12

[hugoteupel]

I’m writing math and physics exams this semester and I can say it’s all self-taught thanks to you😂much love

[gokuldath]

You're the best in the business, thank you

[samirouhani]

Thanks a lot. Just one point, from what I've been studying, I've learned that the AST only tells us whether an alternating series is convergent or not, and it doesn't tell us anything about its divergence.

[risinglabyrinth]

You scared me on question four of the comprehension test, you had me thinking I was supposed to tetrate XD! Thanks for these videos Professor Dave, these actually really help and give some intuition on these topics.

[choo]

I honestly can't believe I've purchased a $150 textbook for contents that could be boiled down in 2 days worth of lecture videos. I'm not saying textbook is useless. But textbook has its limit as it cannot show the reader animations of how some things are done.
Textbook is really only needed for practice problems.

[rolofiend]

You're actually a savior. Holy moly.

[allo]

Hope you're doing well Professor ☺️

[unknownbeing]

Im now studying mathematics lol, i never thought i would do this.

[gp]

Very interesting - always enjoy your videos - thank you

[zhoud]

Great lectures, really enjoyed them. thanks

[roronoazoro]

At the example at 4:38 the number 1/5 = 0.2 and 4/12 = 0.3 which is larger. The terms don't get smaller. How can this series converge?

[subforsubcommunitycenter]

Please add all the details about limits

[Nemoguzapomnit]

Thx a lot fot that video! About problems at the end of the video: Σ[(-2)^n/3^n] is it relevant just to rewrite it as Σ[(-2/3)^n] and say that: as r=-2/3 and its less then 1, then the serires is converges?

[honeydevaang]

so as i understand, the alternative series and all the series associated with the calculus, we only need to find if they are convergent or divergent. but why do we have to do so? what is the relevance of convergence and divergence? maybe it could sound silly but this is my first interaction with the calculus so please pardon me for that.

[yurijettsielk]

thank u so u did a fantastic job teaching us <3

[محمودحقياسماعيلرشيد]

the minute 4:40 it is not 16/70 it is 16/68

[sciencedude]

how does the sum of (-1)^(n-1)/n converge if the sum of 1/n diverges?