Alternating series test | Series | AP Calculus BC | Khan Academy

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When a series alternates (plus, minus, plus, minus,...) there's a fairly simple way to determine whether it converges or diverges: see if the terms of the series approach 0.

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[NutyRiver]

I have a test on this tomorrow! Perfect timing for upload

[ebercota]

It would be nice if you did videos on trick questions of each topic you do. Thanks!!

[Algebrainiac]

5:38 okay so I kind of disagree with how you said this… if the series doesn’t pass the alternating series test, then either one or both of the requirements for convergence are not satisfied. So the series would then diverge…

However if it’s let’s say one that does not look like an alternating series, then obviously we wouldn’t use alternating series test to show if it converges or diverges. It’s important to carefully look at what kind of series you’re dealing with to know what test you’re going to apply. If I am wrong please do correct me but that’s how I see it…

[yanhesapmustafa]

bn doesn't have to be decreasing. take bn=-1.[(1/2)^(n-1)] for example. it is an increasing sequence but the alternating comparison test still applies.

[picorrow]

Haha, I'm just about to have a quiz on this, and I'm glad your video arrived just one time!

[neagucristian]

This doesnt work with the limit comparison test right?

[atharvsawant]

Can you please start a series of math videos on rigorous proofs in real analysis? I find it way to hard to understand because of it's abstract nature