Answer
$\frac{1413}{999}$
Work Step by Step
$1\overline{.414}=1+ \sum_{k=0}^\infty \frac{414}{1000}(\frac{1}{10^{3}})^{k}$
$=1+\frac{(\frac{414}{1000})}{1-(\frac{1}{1000})}=1+\frac{414}{999}$
$=\frac{1413}{999}$
Thomas' Calculus 13th Edition
by Thomas Jr., George B.
Published by
Pearson
ISBN 10:
0-32187-896-5
ISBN 13:
978-0-32187-896-0
Chapter 10: Infinite Sequences and Series - Section 10.2 - Infinite Series - Exercises 10.2 - Page 579: 24
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