Answer
Diverges
Work Step by Step
Given: $\lim\limits_{n \to \infty} a_n=\infty$
In order to define this series, we will take the help of n-th term test.
This test states that when $\lim\limits_{n \to \infty} a_n \ne 0$, the series $\Sigma_{n=1}^{\infty} a_n$ diverges.
Hence, the given series $\Sigma _{n=1}^\infty a_n$ diverges by n-the term test of divergence.
