Cauchy condensation test
= Cauchy condensation test
{c}
{wiki}
If $(a_n)$ is a nonnegative decreasing <sequence>, then $\sum_{n\geq1}a_n$ converges if and only if the condensed series $\sum_{k\geq0}2^ka_{2^k}$ converges. Comparing each dyadic block with its first and last terms proves both directions.