Answer
$$\frac{2}{9}$$
Work Step by Step
Let
$$
x=0 . \overline{2}=0.22222 \ldots
$$
Then
\begin{aligned} 10 x-x &=2.22222 \cdots-0.22222 \cdots \\ 9 x &=2 \\ x &=\frac{2}{9} \end{aligned}
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: 37
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