Chapter 10 - Section 10.1 - Sequences and Summation Notation - Exercise Set - Page 1048: 40

$=\dfrac{-19}{30}$

Here, we have $\sum_{i=0}^4\dfrac{(-1)^{i+1}}{(i+1)!}=\dfrac{(-1)^{0+1}}{(0+1)!}+\dfrac{(-1)^{1+1}}{(1+1)!}+\dfrac{(-1)^{2+1}}{(2+1)!}+\dfrac{(-1)^{3+1}}{(3+1)!}+\dfrac{(-1)^{4+1}}{(4+1)!}$ $=-\dfrac{1}{1}+\dfrac{1}{2}-\dfrac{1}{6}+\dfrac{1}{24}-\dfrac{1}{120}$ $=\dfrac{-120+60-20+5-1}{120}$ $=\dfrac{-19}{30}$