Camp exam problem 3

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*Mahi*
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Camp exam problem 3

Unread post by *Mahi* » Fri Nov 04, 2011 11:31 pm

Let $a;b;c;d$ be positive numbers. Prove that,
\[1 < \frac{a}{a+b+d} + \frac{b}{a+b+c} +\frac{c}{b+c+d} +\frac{d}{a+c+d} < 2\]
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nafistiham
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Re: Camp exam problem 3

Unread post by nafistiham » Sat Nov 05, 2011 12:45 am

needs just 2 crux moves.those are the first and the last move. :D
$1.$
\[\frac{a}{a+b+c+d}+\frac{b}{a+b+c+d}+\frac{c}{a+b+c+d}+\frac{d}{a+b+c+d}=1\]
$2.$
\[\frac{a}{a+b}+\frac{b}{a+b}+\frac{c}{c+d}+\frac{d}{c+d}=2\]

i don't know should have i hidden these.but though did it if someone who hasn't done it yet would like to catch out the second one by seeing the first one or vice versa.

POSTING THIS I GIVE A SPECIAL THANKS TO A GOOD FRIEND OF MINE.
\[\sum_{k=0}^{n-1}e^{\frac{2 \pi i k}{n}}=0\]
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