The series is .

I attempted the ratio test with lim n→∞ of:

and for me this means that L>1 if evaluated when lim n→∞, and so not convergent at all. However, the problem clearly states to determine whether the series converges absolutely or conditionally - hence why my conclusion obviously has to be wrong, and I am making some sort of mistake. I hope you guys can help me see what I'm doing wrong here.

Thank you for your time!