College Algebra (6th Edition)

Published by Pearson
ISBN 10: 0-32178-228-3
ISBN 13: 978-0-32178-228-1

Chapter 8 - Sequences, Induction, and Probability - Exercise Set 8.1 - Page 714: 39


$\displaystyle \frac{3}{8}$

Work Step by Step

The sum has five terms, for i=0,1,2,3,4,5. with alternating signs, of which the first is a plus, $(-1)^{0}=+1.$ The denominators progress as $0!,1!,2!, 3!,4!$ that is as 1, 1, 2, 6, 24. Sum = $+\displaystyle \frac{1}{1}-\frac{1}{1}+\frac{1}{2}-\frac{1}{6}+\frac{1}{24}$ $=\displaystyle \frac{1}{2}-\frac{1}{6}+\frac{1}{24}=\frac{12-4+1}{24}=\frac{9}{24}=\frac{3}{8}$
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