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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.


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

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