# Inequality from [SL 1995 UKR]

• Let $n\ge3$.Let $a_1,a_2,..,a_n$ be positive real numbers such that $2\le{a_i}\le3$ for $i=1,2..,n$ and let $S=a_1+a_2+...+a_n$.Prove that $\sum_{i=1}^{n}\left(\frac{a_i^2+a_{i+1}^2-a_{i+2}^2}{a_i+a_{i+1}+a_{i+2}}+2\right)\le2S$
with $a_1=a_{n+1}$ and $a_2=a_{n+2}$.

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