What should I compare $\displaystyle \sum_{n \ge 0} \frac 1{n!}$ if the question requires me to prove its convergence/divergence using the direct comparison test. I know it converges. It seems like $\displaystyle \frac 1{n!} < \frac 1{n^2}$ for $\displaystyle n \ge 4$, and $\displaystyle \frac 1{n^2}$ converges by p-series test. The first four terms are obviously finite. Is that enough? Is there a better series to compare it to?