Answer
Convergent
Work Step by Step
Given: $\Sigma_{n=1}^\infty\frac{(-1)^{n}}{\sqrt {n+1}}$
Here, $b_{n}= \frac{1}{\sqrt {n+1}}$
$b_{n}= \frac{1}{\sqrt {n+1}}$ is decreasing $\sqrt {n+1}$ is increasing.
Also,
$\lim\limits_{n \to \infty}b_{n}=\lim\limits_{n \to \infty}\frac{1}{\sqrt {n+1}}=\frac{1}{\sqrt {\infty+1}}=0$
Hence, the series is convergent by Alternating Series Test.