Prove that the series $\displaystyle \sum_1^{\infty} \frac{x^n}{n^2}$ converges uniformly on $\displaystyle [-1,1].$
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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
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