Convergence of Series Overview | Known Series, Necessary Criterion & Convergence Criteria
A series converges if it has a limit. That is, if the sum of all terms in the sequence, in exactly the given order, takes on exactly one finite value. To test the convergence of series, there is a fixed sequence of steps you can follow. You'll learn what these are in this video!
CORRECTION: 9:15 "It may be that the sequence of quotients |a_(k+1)/a_(k)| diverges because it has multiple cluster points, but the series still converges." This does NOT refer to the sequence a_(k), as that would contradict the necessary criterion from step 2. Thanks to @kolo toté for the tip :)
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Contents:
0:00 Step-by-Step Guide to Checking Convergence
0:52 Geometric Series
2:36 Harmonic Series
4:06 Telescopic Series
4:57 Necessary Criterion
7:02 Convergence Criteria
7:46 Quotient Criterion
10:11 Root Criterion
11:02 Leibniz Criterion
12:12 Compaction Criterion
12:59 Majorant and Minorant Criterion
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