Multivariable Calculus, 7th Edition

Published by Brooks Cole
ISBN 10: 0-53849-787-4
ISBN 13: 978-0-53849-787-9

Chapter 11 - Infinite Sequences and Series - 11.2 Exercises: 51


$0.888888 = \frac{8}{9}$

Work Step by Step

$0.88888$ $=\frac{8}{10} +\frac{8}{10^{2}}+\frac{8}{10^{3}}+...$ $=\Sigma^{\infty}_{n=1} \frac{8}{10} (\frac{1}{10})^{n-r}$ $a=\frac{8}{10}$ and $r=\frac{1}{10}$ Therefore $0.8888 = \frac{a}{1-r}$ $=\frac{\frac{8}{10}}{1-\frac{1}{10}}$ $=\frac{8}{9}$
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