Answer
$\displaystyle \sum_{k=1}^{∞}(\frac{1}{10})^k=\frac{1}{9}$
Work Step by Step
$\displaystyle \sum_{k=1}^{∞}(\frac{1}{10})^k=\frac{1}{10}+\frac{1}{100}+\frac{1}{1000}+\frac{1}{10000}+...=0.1+0.01+0.001+0.0001+...=0.1111...=\frac{1}{9}$
Algebra and Trigonometry 10th Edition
by Larson, Ron
Published by
Cengage Learning
ISBN 10:
9781337271172
ISBN 13:
978-1-33727-117-2
Chapter 11 - 11.1 - Sequences and Series - 11.1 Exercises - Page 778: 94
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