Convergence of Alternating Series
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In Probability,
$$ \sum\limits_{n=1}^{\infty} {(-1)^n a_n} $$
Check for two things:
- $a_k \geq a_{k+1}, ~ \forall k \in \mathbb{Z}$
- $\lim_{n \to \infty} a_n = 0$
If both of them are true, then the series converges.