Calculus: Early Transcendentals (2nd Edition)

Published by Pearson
ISBN 10: 0321947347
ISBN 13: 978-0-32194-734-5

Chapter 8 - Sequences and Infinite Series - 8.3 Infinite Series - 8.3 Exercises: 51

Answer

$=\dfrac {152}{333}$

Work Step by Step

$0.\overline {456}=0.4656456\ldots =\dfrac {456}{1000}+\dfrac {456}{1000^{2}}+\dfrac {456}{1000^{3}}\ldots =\dfrac {a_{1}}{1-r}=\dfrac {\dfrac {456}{1000}}{1-\dfrac {1}{1000}}=\dfrac {456}{999}=\dfrac {152}{333}$
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