Geometric Series

$$s = 1 + r + r^2 + r^3 + \ldots = \frac{1}{1-r}$$

Explanation

$$s = 1 + r + r^2 + r^3 + \ldots$$

$$rs = r + r^2 + r^3 + \ldots$$

$$s-rs = 1$$

$$s(1-r) = 1$$

$$s = \frac{1}{1-r}$$