Convergence of an infinite series

Question

Does the series $\displaystyle\sum_{n \geq 1} \frac{1}{n^{2 + \sin n}}$ converge? Why?

It seems as if this series will converge since $2 + \sin n > 1$ for all integers $n$, but since $2 + \sin n$ is arbitrarily close to $1$ for some $n$ I cannot immediately use a comparison test.

The series diverges. This is addressed by the same technique as the first of the two series mentioned in my answer here. — Andrés E. Caicedo, Oct 05 '13 at 03:02

score 1 · Answer 1 · edited Apr 13 '17 at 12:21

1

As pointed out in the comments, the series diverges. An overview of the in-depth approach can be found in this answer, which links to a paper with a general approach for this type of series.

edited Apr 13 '17 at 12:21

Community

1

answered Nov 08 '13 at 04:41

apnorton

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Convergence of an infinite series

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