Proof: if $|a|<1$ then $a^n$ converges to $0$

Question

I'm trying to proof a basic statement:

if $|a| < 1$, $a\in \mathbb{R}$ then $\lim_{n\rightarrow \infty } a^n = 0$.

On one hand, it's quite intuitive, on the other hand, I wasn't able to prove it formally. Is this statement needs to be proved or it's some kind of convention?

Thank you.