$\frac{1}{\sqrt{n^3 + 2n}} < \frac{1}{n^{3/2}}$ and $\sum \frac{1}{n^{3/2}}$ converges, so original converges

$\frac{1}{\sqrt{n^3 + 2n}} > \frac{1}{n}$ and $\sum \frac{1}{n}$ converges, so original converges

$\frac{1}{\sqrt{n^3 + 2n}} < \frac{1}{n}$ and $\sum \frac{1}{n}$ diverges, so original diverges

No valid direct comparison can be established