Answer
Converges by Theorem 9.14
Work Step by Step
Rewrite Summation, $\Sigma^{\infty}_{n=1} \frac{(-1)^n}{n!}$
Apply Alternating Series Test
i.)$ \lim\limits_{n \to \infty} \frac{1}{n!} =0$
ii.) $a_{n+1} = \frac{1}{(n+1)!} \leq \frac{1}{n!} = a_n$
Series Converges by Theorem 9.14
