Answer
The series $\Sigma_{n=1}^{\infty} \frac{1}{n+\sqrt n} $ diverges.
Work Step by Step
The series $\Sigma_{n=1}^{\infty} \frac{1}{n }$ is a divergent p-series with $p= 1$. Now, by using the limit comparison test, we have:
$$\lim_{n\to \infty} \frac{(1/(n+\sqrt n))}{1/n}=\lim_{n\to \infty} \frac{n}{n+\sqrt n}=1\gt0.$$
Hence, the series $\Sigma_{n=1}^{\infty} \frac{1}{n+\sqrt n} $ diverges.
