Chapter 12.4, Problem 30AE

Use mathematical induction to prove that if $r\ne 1$, then

$a\text{ + }ar\text{ + }a{r}^{\text{2}}\text{ + }\cdot \cdot \cdot \text{ + }a{r}^{n-1}\text{ = }a\frac{1-r^n}{1-r}$