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