The sum of the series $\frac{1}{2 !}-\frac{1}{3 !}+\frac{1}{4 !}-\ldots$ upto infinity is
The sum of the series $\frac{1}{2 !}-\frac{1}{3 !}+\frac{1}{4 !}-\ldots$ upto infinity is
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$e^{-2}$
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$e^{-1}$
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$\mathrm{e}^{-1 / 2}$
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$\mathrm{e}^{1 / 2}$
Solution
$e^{-x}=1-x+\frac{x^2}{2 !}-\frac{x^3}{3 !}+\frac{x^4}{4 !}-\cdots$
put $x=1$
$\frac{1}{2 !}-\frac{1}{3 !}+\frac{1}{4 !} \cdots=e^{-1}$.
Asked in: JEE Main 2007
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