Sum of reciprocal factorial series

Prove that $e^{- 1} = 2 (\frac{1}{3 !} + \frac{2}{5 !} + \frac{3}{7 !} + \dots)$ .

~10 minProof · checked by AIExponential seriesSeries summation

H. S. Hall & S. R. Knight, Higher Algebra (1891) · Ch. XVII. Exponential and Logarithmic Series, Examples XVII, No. 7

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