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On the convergence of some alternating series

preprint2011arXivOpen access
Angel V. Kumchev
math.NT
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Abstract

We study the convergence sets of a class of alternating series. Among other things, our results establish the convergence of the series ∑n(−1)n∣sin⁡n∣/n\sum_n (-1)^n|\sin n|/n.

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