Compare to $\sum \frac{1}{n^{5/2}}$ and the series diverges.

Compare to $\sum \frac{1}{n^{3/2}}$ and the series converges.

Compare to $\sum \frac{n}{n^3}$ which simplifies to $\sum \frac{1}{n^2}$ and the series converges.

Compare to $\sum \frac{1}{n}$ and the series diverges.