$\sum_{n=1}^{\infty} \frac{1}{n^{1/2}}$

$\sum_{n=1}^{\infty} \frac{1}{n}$

$\sum_{n=1}^{\infty} \frac{1}{n^2}$

$\sum_{n=1}^{\infty} \frac{\ln n}{n^2}$