Limit: $\lim_{n\to \infty} \frac{n^5}{3^n}$ I need help on a homework assignment. How to show that $\lim_{n\to\infty} \left(\dfrac{n^5}{3^n}\right) = 0$? We've been trying some things but we can't seem to find the answer.

Can you complete this?
$n>32 \to n^5<2^n \to \frac{n^5}{3^n}<\frac{2^n}{3^n}$
$n>\log_{\frac32}(\epsilon) \to (\frac32)^n>\epsilon \to (\frac{2}{3})^n<\epsilon$
