I have to assess if $\displaystyle \sum_{n=1}^{ \infty } \frac{1}{1+ n^{2} \cdot x^{2} }$ is convergent (uniformly convergent)

please help

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- May 26th 2012, 09:06 AMfqqsConvergence (series)
I have to assess if $\displaystyle \sum_{n=1}^{ \infty } \frac{1}{1+ n^{2} \cdot x^{2} }$ is convergent (uniformly convergent)

please help - May 26th 2012, 10:08 AMPlatoRe: Convergence (series)
- May 26th 2012, 10:20 AMfqqsRe: Convergence (series)
- May 26th 2012, 10:48 AMPlatoRe: Convergence (series)
- May 26th 2012, 11:05 AMfqqsRe: Convergence (series)
it converges for every $\displaystyle x \ne 0 $

? - May 26th 2012, 11:48 AMPlatoRe: Convergence (series)
- May 26th 2012, 12:18 PMfqqsRe: Convergence (series)
but that only means that it is pointwisely convergent for every $\displaystyle x \ne 0$, yes?

so i need to check if it is pointwisely convergent somewhere , yes?

maybe I should use cases when $\displaystyle |x| < 1$ and when $\displaystyle |x| \ge 1 $ and use Weierstrass? - Jun 1st 2012, 10:33 AMfqqsRe: Convergence (series)
upppp