Algebra and Trigonometry 10th Edition

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


$\displaystyle \sum_{k=1}^{∞}(\frac{1}{10})^k=\frac{1}{9}$

Work Step by Step

$\displaystyle \sum_{k=1}^{∞}(\frac{1}{10})^k=\frac{1}{10}+\frac{1}{100}+\frac{1}{1000}+\frac{1}{10000}+...=0.1+0.01+0.001+0.0001+...=0.1111...=\frac{1}{9}$
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