Uniform convergence of a series

Question

This problem came from the Krantz text ($2^{nd}$ ed. ch. 9, prob. 17): Prove that the series $\displaystyle\sum_{j=1}^{\infty }{\frac{\sin{(jx)}}{j}}$ converges uniformly on compact intervals that do not contain odd multiples of $\displaystyle\frac{\pi}{2}$

Thank you in advance for your help