mateforum.ro

Fie numerele reale \( a_{1},\ a_{2},\ldots,\ a_{n}>1 \) ce satisfac relatia \( \sum_{i=1}^{n}\frac{1}{a_{i}^{2}-1}=1 \). Demonstrati ca \( \sum_{i=1}^{n}\frac{1}{a_{i}+1}\le\frac{n}{\sqrt{n+1}+1} \).

Andrei Razvan Baleanu