Convergence of Alternating SeriesIn Probability, ∑n=1∞(−1)nan\sum\limits_{n=1}^{\infty} {(-1)^n a_n}n=1∑∞(−1)nan Check for two things: ak≥ak+1, ∀k∈Za_k \geq a_{k+1}, ~ \forall k \in \mathbb{Z}ak≥ak+1, ∀k∈Z limn→∞an=0\lim_{n \to \infty} a_n = 0limn→∞an=0 If both of them are true, then the series converges.