Answer
Series Converges by Theorem 9.14
Work Step by Step
Rewrite Summation to identify $a_n$, $\Sigma^{\infty} _{n=0} (-1)^n \frac{1}{(2n+1)!} $
Apply alternating Series Test
i.) $\lim\limits_{n \to \infty} \frac{1}{(2n+1)!} = 0 $
ii.) $ a_{n+1} = \frac{1}{(2n+3)!} \leq \frac{1}{(2n+1)!}= a_n$
The Sum satisfies the conditions and Converges by Theorem 9.14
