Possible Duplicate:
Proving that the sequence $F_{n}(x)=\sum\limits_{k=1}^{n} \frac{\sin{kx}}{k}$ is boundedly convergent on $\mathbb{R}$
From Stewart, we cannot find a calculus 2 easy way to prove this:
$$\sum^{\infty}_{n=1}\frac{\sin[n]}{n}=\frac{1}{2}(\pi-1)$$