Chapter 11 - Infinite Series - 11.2 Summing and Infinite Series - Exercises - Page 547: 23

$$ \frac{8}{7}$$

Given $$ \frac{1}{1}+\frac{1}{8}+\frac{1}{8^{2}}+\cdots$$ Since the series is a geometric series with $|r|=|1/8|<1$, then the series converges and has the sum \begin{align*} S&= \frac{a_1}{1-r}\\ &=\frac{1}{1-\frac{1}{8}}\\ &= \frac{8}{7} \end{align*}