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Does $\sum_{n=1}^{\infty}\sin(n\pi)/n^{2}$ in $\mathbb{C}$ converge or diverge?

My guess is that the series does not converge due to the periodicity of trigonometric functions but I can't be sure without figuring it out more formally.

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    $\sin(n\pi)=0$. Has the question been typed correctly? If so, the seris converges, and has sum $0$, since every term is $0$.2012-01-23

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