# Thread: Convergence and Uniform Convergence

1. ## Convergence and Uniform Convergence

Discuss the convergence ad the uniform convergence of the series $\sum \frac {1} {n^2 x^2}$.

2. It converges whenever x is not 0.
It uniformly converges in $\{x:\left|x\right|>\delta\}\text{ for any }\delta >0$

3. Shanks,can you please further explain to me how to get the set for uniform convergence?

4. $\sum \frac{1}{n^2} = \frac{\pi^2}{6}$
Notice that if x approches 0, $\frac{1}{n^2x^2}$ doesn't tend to 0.