I would use the ratio test. Write out the exponentiation in the denominator, and compare it with the product in the numerator.
Calc Chat Free Solutions
Calculus, 9th Edition, Chapter 9, Section 1, Excercise 53
I don't understand the solution, or how they proved it was zero. In section 9.1 of my book, the only theorems discussed are The Squeeze Theorem, The Absolute Value Theorem, and the Bounded Monotonic Sequence Theorem.