#1499 · Algebra · Linear equations

Factorial Series Identity for Even n

Prove that if $n$ be an even integer, $\frac{1}{1 ! ( n - 1 )!} + \frac{1}{3 ! ( n - 3 )!} + \frac{1}{5 ! ( n - 5 )!} + \dots + \frac{1}{( n - 1 )! 1 !} = \frac{2 ^{n - 1}}{n !}$ .

~15 minProof · checked by AIBinomial CoefficientsCombinatorial Identities

H. S. Hall & S. R. Knight, Higher Algebra (1891) · Ch. XIV. Binomial Theorem: Any Index, Examples XIV.c, No. 17

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