Question 83
Prove that the sum of the elements in any finite subset of the set
$$
\left\{ \frac{1}{mn(m+n+1)} : m, n = 1, 2, 3, \dots \right\}
$$
is less than 2.
$$
\left\{ \frac{1}{mn(m+n+1)} : m, n = 1, 2, 3, \dots \right\}
$$
is less than 2.
MathNet 2026 — Part 06 Question 83
Math Olympiad Vault · MathNet 2026 — Part 06