Alternating Series Test

This calculus 2 video tutorial provides a basic introduction into the alternating series test and how to use it to determine the convergence and divergence of a series.

Remainder Estimate - Integral Test:

P-Series:

Direct Comparison Test:

Limit Comparison Test:

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Alternating Series Test:

Alternate Series Estimation Theorem:

Absolute & Conditional Convergence:

The Ratio Test:

The Root Test:

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Series Tests - Practice Problems:

Taylor & Maclaurin Polynomials:

Taylor's Remainder Theorem:

Power Series - Interval Convergence:

Power Series - Derivatives & Integrals:

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Calculus Final Exam and Video Playlists:

Full-Length Videos and Worksheets:

[itllbeokay]

You've got this. Stop reading comments and go study to ace that test.
Or pass that test whatever your goal is

[meerasrinivasan]

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[luciogaribay]

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[hsc]

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[ahmedjamshaid]

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[nurayim]

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[zhouj]

I love all of your videos. They help me a lot. I just want to point out one thing in this video: at the 6 minutes mark, you said :”The test is failed, so the series diverges.” Alternating series test just can prove convergence, can not prove divergent. So the conclusion should be inconclusive. If the test failed, we should use other test to define convergence or divergent.

[itsharukadayo]

I was about to cry because I didn't understand a word until I watched this video
THANK YOU THREE YEARS LATER!!

[joshuaabbott]

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[liquidice]

GREAT VIDEO!!!! Also a note is that this video is about conditional convergence. Alternate series can converge in a different manner known as absolute convergence, and the test for that is if the absolute value of an alternating series (an) converges, then the series converges absolutely and you dont need to check for conditional convergence.

[chrisp]

Between your videos and Paul's Notes for additional practice problems, I have an A+ in calculus 2. Thank you!

[adabujiki]

Lol this guy knows my deep frustrations with this concept-- I COULD NEVER FIGURE OUT WHAT A-sub-n was in the function... turns out it was the quotient 1/n... when one sees a bunch of "n" variables everywhere it is hard to tell how to solve it. THANKS BRO... be nice to show ur face one day so we can profile u and make assumptions of u

[rapr]

It would be more accurately described as it needs to fail the divergence test. As passing the test implies its divergent. Other than that excellent video

[rotemlv]

10:21
n has to go from 2 here as the denominator is undefined at n = 1.

[Just_A_Transperson]

Thank you so much. You got me a 5 on AP calc, and you care getting me through calc 2 in collage.

[rajendramisir]

Interesting: Harmonic series diverges by p-series test while alternating harmonic series converges by alternating series test.

[hibanazar]

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Thank you so much.

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[nothingtoxicated]

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