Answer
Diverges
Work Step by Step
Consider $u_n=(-1)^{n+1}\dfrac{3\sqrt{n+1}}{\sqrt n+1}$
Here, $u_n$ is positive for all the values of $n$.
Now $\lim\limits_{n \to \infty}\dfrac{3\sqrt{n+1}}{\sqrt n+1}=3\ne 0$
Hence, the series diverges by the nth Term Test.