Inequality for all positive reals
Source: Balkan MO ShortList 2008 A1
April 5, 2020
Inequalityinequalities
Problem Statement
For all , Prove
\begin{align*} \sum \frac{1}{2\nu \alpha_1 +\alpha_2+\alpha_3} > \frac{2\nu}{2\nu +1} \left( \sum \frac{1}{\nu \alpha_1 + \nu \alpha_2 + \alpha_3} \right) \end{align*}
for every positive real number