Discuss the convergence ad the uniform convergence of the series $\displaystyle \sum \frac {1} {n^2 x^2}$.
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It converges whenever x is not 0. It uniformly converges in $\displaystyle \{x:\left|x\right|>\delta\}\text{ for any }\delta >0$
Shanks,can you please further explain to me how to get the set for uniform convergence?
$\displaystyle \sum \frac{1}{n^2} = \frac{\pi^2}{6}$ Notice that if x approches 0, $\displaystyle \frac{1}{n^2x^2}$ doesn't tend to 0.
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