$\sum_{n=1}^{\infty} \frac{1}{n}$ (diverges by p-series test)

$\sum_{n=1}^{\infty} \frac{1}{n^2}$ (converges by p-series test)

$\sum_{n=1}^{\infty} \frac{n}{n^5}$ (same as $\sum 1/n^4$, converges)

$\sum_{n=1}^{\infty} \frac{n^2}{n^5}$ (same as $\sum 1/n^3$, converges)