## Calculus (3rd Edition)

Published by W. H. Freeman

# Chapter 11 - Infinite Series - 11.2 Summing and Infinite Series - Exercises - Page 548: 39

#### Answer

$$\frac{31}{99}$$

#### Work Step by Step

Let $$x=0 . \overline{31}=0.313131 \ldots$$ Then \begin{aligned} 100 x-x &=31.313131\cdots \cdots-0.313131\cdots \\ 99 x &=31\\ x &=\frac{31}{99} \end{aligned}

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