Prove that the series

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

converges uniformly on $\displaystyle [-1,1].$

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- Nov 30th 2009, 04:04 PMAnonymous1uniform convergence of a series.
Prove that the series

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

converges uniformly on $\displaystyle [-1,1].$ - Nov 30th 2009, 05:12 PMJose27
If $\displaystyle x\in [-1,1]$ then $\displaystyle \vert \frac{x^n}{n^2} \vert \leq \frac{1}{n^2}$ and use Weierstrass M-test