Answer
$S_{1}=1;$
$S_{2}=S_{1}-\dfrac {1}{2}=\dfrac {1}{2};$
$S_{3}=S_{2}+\dfrac {1}{6}=\dfrac {2}{3};$
$S_{4}=S_{3}-\dfrac {1}{24}=\dfrac {5}{8};$
$S_{5}=S_4+\frac{1}{120}=\frac{19}{30}$
Work Step by Step
$S_{n}=\sum ^{n}_{n=1}\dfrac {\left( -1\right) ^{n+1}}{n!}\Rightarrow $
$S_{1}=1;$
$S_{2}=S_{1}-\dfrac {1}{2}=\dfrac {1}{2};$
$S_{3}=S_{2}+\dfrac {1}{6}=\dfrac {2}{3};$
$S_{4}=S_{3}-\dfrac {1}{24}=\dfrac {5}{8};$
$S_{5}=S_4+\frac{1}{120}=\frac{19}{30}$
