I need to prove that $f(x)= \sum_{n=1}^{\infty} \frac{\sin nx + \cos nx }{n^3}$ is well defined on $\mathbb{R}$, is a differentiable function, and it's derivative is differentiable continuous.
I used Weierstrass's M-Test and proved that the series uniformly converges (since it is smaller than $\sum_{0}^{\infty}\frac{2}{n^3}$- Is it enough?) so it's differentiable, How do I check wheter $f$ continuous or not?
$x$ is all the real line.
Thanks a lot!