Convergence of Infinite Series
Warning
This post is more than a year old. Information may be outdated.
In Probability,
$\sum\limits_{n=1}^{\infty} a_n$ converges if and only if the partial sum $S_N = \sum\limits_{n=1}^{N} a_n$ converges to a finite $S_N \to S$ and $S$ is finite.