- Thread starter
- Moderator
- #1
- Jan 26, 2012
- 995
Thanks again to those who participated in last week's POTW! Here's this week's problem!
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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:
Remember to read the POTW submission guidelines to find out how to submit your answers!
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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:
Consider the term for $k=m$ in the binomial theorem expansion for $(x+y)^{m+n}$ for appropriate $x$ and $y$.
Remember to read the POTW submission guidelines to find out how to submit your answers!