Answer
Diverges
Work Step by Step
Let $u_n=\dfrac{1}{n+\sqrt n}$ and $v_n=(\dfrac{1}{n})$
Now, $\lim\limits_{n \to \infty}\dfrac{u_n}{v_n} =\lim\limits_{n \to \infty}\dfrac{\dfrac{1}{n+\sqrt n}}{(\dfrac{1}{n})}$
$\implies \lim\limits_{n \to \infty} \dfrac{n}{n+\sqrt n}=\lim\limits_{n \to \infty} \dfrac{1}{1+\sqrt n/n}=1$
Hence, the series diverges due to the limit comparison test.