$\displaystyle \sum_{n=1}^{{\color{red}\infty}}r^n$

I'm assuming this is the correct way to write;

$\displaystyle r+r^2+r^3+r^4 . . . r^n$ where the n goes on for infinity.

So how can you prove;

$\displaystyle \sum_{n=1}^{{\color{red}\infty}}r^n = \frac{r}{1-r}$