BALKAN-SL 2010 A3

Let $a,b,c,d$ be positive real numbers. Prove that $(\frac{a}{a+b})^{5}+(\frac{b}{b+c})^{5}+(\frac{c}{c+d})^{5}+(\frac{d}{d+a})^{5}\ge \frac{1}{8}$

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