If $\sum a_{n}$ is a series of positive real terms and $$\sqrt[n]{a_{n}} < k < 1$$ for all $n > N$ , then $\sum a_{n}$ is convergent. If $\sqrt[n]{a_{n}} \geq 1$ for an infinite number of values of $n$ , then $\sum a_{n}$ is divergent.

Limit form