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Determine whether the sum converges $\sum\limits_{n=1}^{\infty} \frac{\sin^n(n)}{n} $

I tried to use all the standard signs, but there's nothing to understand about them in general. It seems to me that the problem is connected with the approximation of the number pi by rational numbers, but I could not bring this idea to the end.

Gabriel Romon
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Vladislav Kharlamov
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    Related: https://math.stackexchange.com/questions/823816/is-sum-limits-n-1-infty-frac-sin-nnn-convergent and https://math.stackexchange.com/questions/811717/does-the-sequence-sinnn-converge/ – Gabriel Romon May 08 '18 at 20:43
  • Thanks you!.... – Vladislav Kharlamov May 08 '18 at 20:46
  • In fact, the question is a duplicate of https://math.stackexchange.com/questions/328306/convergence-of-the-series-sum-n-1-infty-frac-sin-nnn . But since the latter has been left unanswered, I don't think yours should be closed. – Gabriel Romon May 08 '18 at 20:48

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