Algebra and Trigonometry 10th Edition

Published by Cengage Learning
ISBN 10: 9781337271172
ISBN 13: 978-1-33727-117-2

Chapter 11 - Review Exercises - Page 841: 53


$\displaystyle \sum_{i=1}^{4}(\frac{1}{2})^i=\frac{15}{16}$

Work Step by Step

$\displaystyle \sum_{i=1}^{4}(\frac{1}{2})^i=\displaystyle \sum_{i=1}^{4}\frac{1}{2}(\frac{1}{2})^{i-1}$ $a_1=\frac{1}{2}$ $r=\frac{1}{2}$ $S_n=a_1(\frac{1-r^n}{1-r})$ $S_4=\frac{1}{2}(\frac{1-(\frac{1}{2})^4}{1-\frac{1}{2}})=(\frac{1}{2})\frac{1-\frac{1}{16}}{\frac{1}{2}}=(\frac{1}{2})\frac{\frac{15}{16}}{\frac{1}{2}}=\frac{15}{16}$
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