Answer
The series is convergent
Work Step by Step
$\Sigma^{\infty}_{n=1} \frac{(-1)^{n-1}}{n!}$
$a_{n}=\frac{(-1)^{n-1}}{n!}$
partial sum $s_{n}=a_{1}+a_{2}+...+a_{n}$
$n=1$ $a_{1}=1.000$ $s_{1}=1.000$
$n=2$ $a_{2}=-0.500$ $s_{2}=0.500$
$n=3$ $a_{3}=0.16667$ $s_{3}=0.6667$
$n=4$ $a_{4}=-0.04167$ $s_{4}=0.6250$
$n=5$ $a_{5}=0.00833$ $s_{5}=0.6333$
$n=6$ $a_{6}=-0.00139$ $s_{6}=0.6319$
$n=7$ $a_{7}=0.00020$ $s_{7}=0.6321$
$n=8$ $a_{8}=-0.00002$ $s_{8}=0.6321$
The series appears to be converging to approximately $0.6321$
