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