1-31!+92!-273!+……∞1+91!+812!+7293!+…∞=

1-31+92-273 + ⋯⋯ ∞×1+91+812+7293+⋯⋯ =e-3×e9=e6

1-31!+92!-273!+……∞1+91!+812!+7293!+…∞=

1-31+92-273 + ⋯⋯ ∞×1+91+812+7293+⋯⋯ =e-3×e9=e6

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$(1 - \frac{3}{1!} + \frac{9}{2!} - \frac{27}{3!} + \dots \dots \infty) (1 + \frac{9}{1!} + \frac{81}{2!} + \frac{729}{3!} + \dots \infty) =$

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Detailed Solution

$\begin{array}{rcl} (1 - \frac{3}{1} + \frac{9}{2} - \frac{27}{3} + \dots \dots \infty) \times (1 + \frac{9}{1} + \frac{81}{2} + \frac{729}{3} + \dots \dots) \\ = & e^{- 3} \times e^{9} = e^{6} \end{array}$

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