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I'm almost sure that the series $\sum \sin^n(n)$ is not convergent, but lack proof. Thank for any help.

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    Maybe these answers could help you:http://math.stackexchange.com/questions/109029/convergence-divergence-of-infinite-series-sum-n-1-infty-frac-sinn2 , http://math.stackexchange.com/questions/2270/convergence-of-sum-limits-n-1-infty-sinnk-n.2012-04-02

3 Answers 3