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 548: 40


$$\frac{217}{999} $$

Work Step by Step

Let $$x= 0.217217217\cdots $$ Then \begin{align*} 1000x-x&= 217.217217217\cdots-0.217217217\cdots \\ 999x&=217\\ x&=\frac{217}{999} \end{align*}
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