Answer
$\frac{1}{99}$
Work Step by Step
$0.\overline {01}=0.010101\ldots =\dfrac {1}{100}+\dfrac {1}{100^{2}}+\dfrac {1}{100^{3}}\ldots =\dfrac {a_{1}}{1-r}=\dfrac {\dfrac {1}{100}}{1-\dfrac {1}{100}}=\dfrac {1}{99}$
Calculus 10th Edition
by Larson, Ron; Edwards, Bruce H.
Published by
Brooks Cole
ISBN 10:
1-28505-709-0
ISBN 13:
978-1-28505-709-5
Chapter 9 - Infinite Series - 9.2 Exercises - Page 601: 38
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