calculus - Find $lim_{ntoinfty} frac{n^2}{2^n}$

$$\lim_{n\to\infty}\frac{n^2}{2^n}$$

Do you have some tips so I could solve this problem, without the use of L'Hôpital's rule?
Indeed, we didn't see formally L'Hôpital's rule, nor Taylor series so I'm supposed to do this without such "tools".

I've tried using the fact that
$n^2 = e^{2\log(n)}$ and $2^n=e^{n\log(2)}$ but didn't manage to eliminate my indeterminate form.

Thanks in advance.

Answer

There are many ways to do that. For example, you can prove that for $n \ge 10$ we have

$$2^n > n^3.$$
You can show that using the induction argument.