# Lim of An=n^2*exp(-sqrt(n))

by oferon
Tags: ann2expsqrtn
 P: 30 Hi all, my problem regards this limit: $$\lim_{n\to\infty}n^2e^{(-\sqrt{n})}$$ Obviously equals 0, but I can't find how to show it. Tried the squeeze theorem (coudn't find any propriate upper bound) Ratio test won't seem to work.. I do realize the reason for that is that the set approaches 0 starting at heigher n's.. Anyway.. how can I prove convergence and find the limit in a formal way? thanks!