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

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

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

$\sum_{n=1}^{\infty} \frac{1}{n^{3/2}}$