AT-OEMO-FED1 2021 Problem 1

Let $a,b,c\geq 0$ and $a+b+c=1.$ Prove that $\frac{a}{2a+1}+\frac{b}{3b+1}+\frac{c}{6c+1}\leq \frac{1}{2}.$ (Marian Dinca)

Dataset text AI-MO AoPS. Quoted with source.

Solutions

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