## Calculus (3rd Edition)

Published by W. H. Freeman

# Chapter 11 - Infinite Series - 11.2 Summing and Infinite Series - Exercises - Page 548: 41

#### 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*}

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