# Chapter 11 - Infinite Sequences and Series - 11.2 Series - 11.2 Exercises - Page 755: 8

The series appears to be converging to approximately $0.6321$

#### 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 $0.6321$

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