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  4. The sum of the series (1/2!)-(1/3!)+(1/4!)-... upto infinity is

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Q. The sum of the series $\frac{1}{2!}-\frac{1}{3!}+\frac{1}{4!}-...$ upto infinity is

AIEEEAIEEE 2007Sequences and Series

Solution:

$e^{-x}=1-x+\frac{x^{2}}{2!}-\frac{x^{3}}{3!}+\frac{x^{4}}{4!}-...$
put $x = 1$
$\frac{1}{2!}-\frac{1}{3!}+\frac{1}{4!}...=e^{-1}.$