$\frac {a_{n+1}}{a_n} \le \frac {b_{n+1}}{b_n}$ If $\sum_{n=1}^\infty b_n$ converges then $\sum_{n=1}^\infty a_n$ converges as well
Prove if $|a_{n+1}|/|a_n| \leq |b_{n+1}|/|{b_n}|$ and $\sum |b_n|$ is convergent, then $\sum |a_n|$ is convergent