Condition

Let $\sum_{n=1}^\infin a_n$ be a series of nonzero terms.

Result

$\sum_{n=1}^\infin a_n$ converges $\lim_{n→\infin}{\sqrt [n]{|a_n|}}<1$

$\sum_{n=1}^\infin a_n$ diverges $\lim_{n→\infin}{\sqrt [n]{|a_n|}}>1$

The test is inconclusive if $\lim_{n→\infin}{\sqrt [n]{|a_n|}}=1$

• ⁍ reference and proof