Geometric Series

A geometric series is a series of numbers where each term after the first is found by multiplying the previous term by a constant called the common ratio.

$$S_n=a+ar+a{r}^2+a{r}^3+...+a{r}^{n-1}=a\frac{1-r^n}{1-r}\text{for }r\ne 1$$

Example

$$\sum _{n=0}^{\infty }{x}^n=\frac{1}{1-x}\text{, for }|x|<1$$