Proof of the power series 1 + $x^2$ + $x^3$ + $ldots$ + $x^n$ = $frac{1}{1-x}$

Can anyone show me the proof of why if $|x|<1$ then:

$$
\lim_{n \to \infty} 1+ x^2 + x^3 + \ldots + x^n = \frac{1}{1-x}
$$