Is there a theorem which says when we can interchange the limit and sum as follow:
$$\lim_{x\to \infty} \sum_{n=1}^{\infty}f(x,n)= \sum_{n=1}^{\infty}\lim_{x\to \infty}f(x,n)$$
Note: In my case the sum $\sum_{n=1}^{\infty}f(x,n)$ is finite at each finite $x\in \mathbb R$.