In other words, how to prove:

> 
> For all real constants $a$ and $b$ such that $a > 1$,
> 
> 
> $$\lim\_{n\to\infty}\frac{n^b}{a^n} = 0$$
> 
> 
> 

I know the definition of limit but I feel that it's not enough to prove this theorem.