College Algebra (6th Edition)

$\displaystyle \frac{3}{8}$
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 = $+\displaystyle \frac{1}{1}-\frac{1}{1}+\frac{1}{2}-\frac{1}{6}+\frac{1}{24}$ $=\displaystyle \frac{1}{2}-\frac{1}{6}+\frac{1}{24}=\frac{12-4+1}{24}=\frac{9}{24}=\frac{3}{8}$