Comparison_Test
Theorem
Assume $\left. \left( a_{k} \right) \right.$ and $\left. \left( b_{k} \right) \right.$ are sequences satisfying $0 \leq a_{k} \leq b_{k}$ for all $k \in \mathbb{N}$.
If $\sum_{k = 1}^{\infty}b_{k}$ converges, then $\sum_{k = 1}^{\infty}a_{k}$ converges.
If $\sum_{k = 1}^{\infty}a_{k}$ diverges, then $\sum_{k = 1}^{\infty}b_{k}$ diverges.