Calculus (3rd Edition)

Published by W. H. Freeman
ISBN 10: 1464125260
ISBN 13: 978-1-46412-526-3

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


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

Work Step by Step

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*}
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