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.