- Thread starter
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- #1

- Jan 26, 2012

- 995

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**Problem**: Prove that

\[\left(\frac{m}{m+n}\right)^m \left(\frac{n}{m+n}\right)^n {{m+n}\choose m}<1\]

for all $m,n\in\mathbb{Z}^+$.

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**Hint:**

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