Calculus (3rd Edition)

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: 42


$$\frac{abc}{999 } $$

Work Step by Step

Let $$x= 0.abcabcabc \cdots $$ Then \begin{align*} 1000x-x&=abc.abcabcabc\cdots-0.abcabcabc\cdots \\ 999x&=abc\\ x&=\frac{abc}{999 } \end{align*}
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