Answer
$\displaystyle \sum_{i=1}^{∞}\frac{2}{10^i}=\frac{2}{9}$
Work Step by Step
$\displaystyle \sum_{i=1}^{∞}\frac{2}{10^i}=\frac{2}{10}+\frac{2}{100}+\frac{2}{1000}+\frac{2}{10000}+...=0.2+0.02+0.002+0.0002+...=0.2222...=\frac{2}{9}$
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: 96
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