olymmath

NZ-NZMO 2024 Problem 2

  • Answer

Prove the following inequality

620243<(1−34)(1−35)(1−36)(1−37)…(1−32025).\frac{6}{2024^{3}} < \left(1 - \frac{3}{4}\right)\left(1 - \frac{3}{5}\right)\left(1 - \frac{3}{6}\right)\left(1 - \frac{3}{7}\right)\dots \left(1 - \frac{3}{2025}\right).

Dataset text NuminaMath olympiads. Quoted with source.

Show the answer

\frac{6}{2024^{3}} < \left(1 - \frac{3}{4}\right)\left(1 - \frac{3}{5}\right)\left(1 - \frac{3}{6}\right)\left(1 - \frac{3}{7}\right)\dots \left(1 - \frac{3}{2025}\right)

Solutions

No solution is on olymmath yet. Official and human solutions come first when they arrive. AI solutions come after them, with a label.

Add a solution

Locator nz-nzmo/2024/p2 · Tag 8D9WKDCK4E · Edit this page on GitHub · Keys: j next, k previous