Fall 2018, problem 74
Prove that, for any real numbers $a_1,a_2, \ldots, a_n$, $\displaystyle\qquad\sum_{i,j=1}^n{\frac{a_ia_j}{i+j-1}}\geq 0$.
Prove that, for any real numbers $a_1,a_2, \ldots, a_n$, $\displaystyle\qquad\sum_{i,j=1}^n{\frac{a_ia_j}{i+j-1}}\geq 0$.