Chapter 11 - Infinite Sequences and Series - 11.2 Exercises - Page 736: 51

$0.888888 = \frac{8}{9}$

$0.88888$ $=\frac{8}{10} +\frac{8}{10^{2}}+\frac{8}{10^{3}}+...$ $=\Sigma^{\infty}_{n=1} \frac{8}{10} (\frac{1}{10})^{n-r}$ $a=\frac{8}{10}$ and $r=\frac{1}{10}$ Therefore $0.8888 = \frac{a}{1-r}$ $=\frac{\frac{8}{10}}{1-\frac{1}{10}}$ $=\frac{8}{9}$