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Question Number 3204 by Filup last updated on 07/Dec/15

\underset{i = 1}{\prod^{n}} i! = 1 \times (1 \times 2) \times \dots \times (1 \times 2 \times \dots \times n)

= 1^{n} 2^{n - 1} 3^{n - 2} \dots {(n - 1)}^{2} n

∴ \underset{i = 1}{\prod^{n}} i! = \underset{i = 1}{\prod^{n}} {(n - i + 1)}^{i}

The above is only for i \in Z

What about :

\underset{i = 1}{\prod^{n}} Γ (i + 1) where i \notin Z

Commented by prakash jain last updated on 07/Dec/15

In the product you are starting with i = 1 and

going up to n . Generally it is increment by

1 so i \in Z .