Math — Convergence Tests

\lim_{n\to\infty}\left|\frac{a_{n+1}}{a_n}\right| = L

L < 1 \Rightarrow \text{converges}

\sum \frac{1}{n^p} \;\;\text{converges} \iff p > 1

\lim_{n\to\infty} a_n \neq 0 \Rightarrow \text{diverges}