MemexConvergence of Alternating SeriesConvergence of Alternating SeriesIn Probability,โn=1โ(โ1)nan\sum\limits_{n=1}^{\infty} {(-1)^n a_n}n=1โโโ(โ1)nanโCheck for two things:akโฅak+1,ย โkโZa_k \geq a_{k+1}, ~ \forall k \in \mathbb{Z}akโโฅak+1โ,ย โkโZlimโกnโโan=0\lim_{n \to \infty} a_n = 0limnโโโanโ=0If both of them are true, then the series converges.