I'm not sure how to prove whether this converges or diverges. I have a hunch that it converges, due to the factorial growing more slowly than an nth root, but I can't figure out how to prove it. The factorial keeps getting in the way.
I did try to take the natural log, but again I wasn't sure how to proceed with the ln. Additionally, I feel like there's a better, more elegant solution. How can I determine this series' convergence?