If some alternating [[Series]] $S$ that takes the form: $\huge \sum^{\infty}_{n-1} (-1)^nb_{n}$ satisfies: 1. $b_{n+1} \ge b_n$ for all $n$ 2. $\lim_{n\to \infty}b_{n} = 0$ Then $S$ [[Convergent Series|Converges]].