Examples (Part 2):
The video below shows how
- ∑(−1)nln(n) converges by the Alternating Series Test (it converges conditionally);
- ∑(−1)n(n+1)2n is an alternating series, but it diverges, since the terms do not approach zero;
- ∑cos(n)n2 converges absolutely, by comparison to ∑1n2;
- ∑n2(23)n converges by the Ratio Test;
- ∑(3/2)nn5 diverges by the Ratio Test;
- ∑(1−1n2)n3 converges by the Root Test.
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