Answer
$$\frac{a}{9 } $$
Work Step by Step
Let $$x= 0.aaaaaaaaaaaaaa\cdots $$
Then
\begin{align*}
10x-x&= a.aaaaaaaaa\cdots-0.aaaaaaaaaa\cdots \\
9x&=a\\
x&=\frac{a}{9 }
\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: 41
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