# What is the Direct Comparison Test for Convergence of an Infinite Series?

If you are trying determine the conergence of $\sum \left\{{a}_{n}\right\}$, then you can compare with $\sum {b}_{n}$ whose convergence is known.
If $0 \le q {a}_{n} \le q {b}_{n}$ and $\sum {b}_{n}$ converges, then $\sum {a}_{n}$ also converges.
If ${a}_{n} \ge q {b}_{n} \ge q 0$ and $\sum {b}_{n}$ diverges, then $\sum {a}_{n}$ also diverges.