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Possible Duplicate:
Proving that the sequence $F_{n}(x)=\sum\limits_{k=1}^{n} \frac{\sin{kx}}{k}$ is boundedly convergent on $\mathbb{R}$

Evaluate $\displaystyle\sum_{k=1}^{\infty}\frac{\sin k}{k}$.

By a calculator, I'm convinced that it convergents, but I'm not sure how to calculate it. Please help. Thank you.

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    @Martin: I was just pointing that out for the benefit of anyone who might be considering voting to close. As it happens, all three who have so far done so have cited that answer.2012-10-21

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