# uniform convergence of a series.

$\sum_1^{\infty} \frac{x^n}{n^2}$
converges uniformly on $[-1,1].$
If $x\in [-1,1]$ then $\vert \frac{x^n}{n^2} \vert \leq \frac{1}{n^2}$ and use Weierstrass M-test