$\sum_{n=1}^{\infty} \frac{\cos^2(n)}{n^2 + n}$ because $0 \leq \frac{\cos^2(n)}{n^2 + n} \leq \frac{1}{n^2}$ for all $n \geq 1$

$\sum_{n=1}^{\infty} \frac{1}{n^3 + n^2}$ because $\frac{1}{n^3 + n^2} > \frac{1}{n^2}$ for all $n$

$\sum_{n=1}^{\infty} \frac{n}{n^3}$ because it equals $\sum \frac{1}{n^2}$

$\sum_{n=1}^{\infty} \frac{\sin(n)}{n^2}$ because $\sin(n) \leq 1$