An alternating series is a series where an flips sign every turn. For instance, ∞∑n=1(−1)nn=1−12+13−14+….
Alternating Series Test: If {bn} is a non-increasing sequence of non-negative numbers with limn→∞bn=0, then ∞∑n=1(−1)n−1bn=b1−b2+b3−b4+… converges.