I suggest first checking that the series converges.

Calcuating a_n for a few large n suggests that the ratio test would be inconclusive (ratio = 1).

Using Raabe's test for few large n suggests that the series may be divergent. However, while Raabe's test can be used to show that a series is convergent I am not sure that the converse is true.

I suspect that one of the convergence tests in your toolbox may show that this series diverges.