Answer
$$\frac{217}{999} $$
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*}
Calculus (3rd Edition)
by Rogawski, Jon; Adams, Colin
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
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