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        riddles >> putnam exam (pure math) >> Factorials
        
(Message started by: THUDandBLUNDER on Dec 6^th, 2004, 12:21am)

Title: Factorials
Post by THUDandBLUNDER on Dec 6^th, 2004, 12:21am

Let m and n be positive integers.

Show that

(m+n)! / (m+n)^(m+n) < (m!)*(n!) / [(m^m) * (nⁿ)]

Title: Re: Factorials
Post by Aryabhatta on Dec 9^th, 2004, 2:16am

The following works:
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Rearrange as
(m+n)!*(m^m)*(n^n)/(m!)*(n!) < (m+n)^(m+n)
and using binomial theorem makes it almost trivial.
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A week away from this forum and wow! So many new puzzles... nice. Should go away more often :D