calculus - Proving that $n over 2^n$ converges to $0$

I'm completely clueless on this one. I can easily calculate the limit using L'Hopital's rule, but proving that the series is converging to 0 is far more tricky.

$$a_n= {n \over 2^n}$$

Any help?

Answer

Using the fact that $2^n>n^2$ for $n > 4$, we have:

$$0 \leq a_n < \frac{n}{n^2}=\frac{1}{n}.$$

Hence, $\displaystyle \lim_{n \to \infty}a_n=0.$