Question 20
Prove that, for any real $a_{1}, a_{2}, \ldots, a_{n}$,
$$
\sum_{i, j=1}^{n} \frac{a_{i} a_{j}}{i+j-1} \geq 0
$$
$$
\sum_{i, j=1}^{n} \frac{a_{i} a_{j}}{i+j-1} \geq 0
$$
MathNet 1990 — Part 01 Question 20
Math Olympiad Vault · MathNet 1990 — Part 01