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For every integer n≥1, let P(n) denote the product of the first n odd numbers:

P(n)=1×3×5×⋯×(2n−1)

Prove that for all integers n≥1, P(n)=(2n)!/2^n×n!.

 Apr 18, 2024
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You can use Stirling's formula:

n! = sqrt(2*pi*n)*(n/e)^n

 Jul 1, 2024

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