Answer
$\frac{-19}{30}$
Work Step by Step
$\sum\limits_{i=0}^4\frac{(-1)^{i+1}}{(i+1)!}=\frac{(-1)^1}{1!}+\frac{(-1)^2}{2!}+\frac{(-1)^3}{3!}+\frac{(-1)^4}{4!}+\frac{(-1)^5}{5!}=\frac{-1}{1}+\frac{1}{2}+\frac{-1}{6}+\frac{1}{24}+\frac{-1}{120}=(-1)+\frac{1}{2}+\frac{-1}{6}+\frac{1}{24}+\frac{-1}{120}=\frac{-120}{120}+\frac{60}{120}+\frac{-20}{120}+\frac{5}{120}+\frac{-1}{120}=\frac{-76}{120}=\frac{-19}{30}$
