Library / Harvard-MIT November Tournament /15 of 74

Harvard-MIT November Tournament

Algebra Difficulty 4.6 AIME Prove it United States

Problem:
Explain how any unit fraction $\frac{1}{n}$ can be decomposed into other unit fractions.

Solution

Solution:
$\frac{1}{n} = \frac{1}{2n} + \frac{1}{3n} + \frac{1}{6n}$

Want a route through all this instead of an archive? The track puts 2,604 problems in a working order, from Junior Challenge level to the IMO shortlist.

Source: MathNet, licensed CC-BY-4.0. Statement reproduced verbatim; metadata (topic, difficulty) added by this project.