I have to solve this problem:

> 
> Show that the series $f(x)=\sum\_{n=1}^{+\infty} \frac{\sin (x n)}{n^\alpha}$
> defines continuous function on $\Bbb R$ for $\alpha>1$."
> 
> 
> 

First of all what I can say is that this series converges since it is smaller than $\frac{1}{n^\alpha}$, so by weierstrass also the first series converges. I don't know how to procede. Have you got any suggestions?