Leibniz Criterion

Also known as the Alternating Series Test. Given a Series

$$\sum_{n=1}^\infty (-1)^{n+1}a_n$$

with $a_n > 0$, if $a_n$ is monotonic decreasing as $n\to \infty$ and

$$\lim_{n\to \infty } a_n = 0,$$

then the series Converges.