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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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marked as duplicate by Norbert, user641, Brian M. Scott, rschwieb, Jason DeVito Oct 21 '12 at 14:20

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