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Infimum and supremum for an expression

Source: Swiss IMO TST 2003

February 27, 2014
inequalities proposedinequalities

Problem Statement

Find the largest real number C1 C_1 and the smallest real number C2 C_2 , such that, for all reals a,b,c,d,e a,b,c,d,e , we have C1<aa+b+bb+c+cc+d+dd+e+ee+a<C2 C_1 < \frac{a}{a+b}+\frac{b}{b+c}+\frac{c}{c+d}+\frac{d}{d+e}+\frac{e}{e+a} < C_2
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