# uniform convergence of a series.

• November 30th 2009, 04:04 PM
Anonymous1
uniform convergence of a series.
Prove that the series

$\sum_1^{\infty} \frac{x^n}{n^2}$

converges uniformly on $[-1,1].$
• November 30th 2009, 05:12 PM
Jose27
If $x\in [-1,1]$ then $\vert \frac{x^n}{n^2} \vert \leq \frac{1}{n^2}$ and use Weierstrass M-test