Inequality from [SL 1995 UKR]



  • Let n3n\ge3.Let a1,a2,..,ana_1,a_2,..,a_n be positive real numbers such that 2ai32\le{a_i}\le3 for i=1,2..,ni=1,2..,n and let S=a1+a2+...+anS=a_1+a_2+...+a_n.Prove that i=1n(ai2+ai+12ai+22ai+ai+1+ai+2+2)2S\sum_{i=1}^{n}\left(\frac{a_i^2+a_{i+1}^2-a_{i+2}^2}{a_i+a_{i+1}+a_{i+2}}+2\right)\le2S
    with a1=an+1a_1=a_{n+1} and a2=an+2a_2=a_{n+2}.


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