Convergence of Alternating Series

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.