MathDB
every rational in (0,1) i sum of 1/k(k+1)

Source: 2023 Swedish Mathematical Competition p6

March 24, 2024
algebranumber theory

Problem Statement

Prove that every rational number xx in the interval (0,1)(0, 1) can be written as a finite sum of different fractions of the type 1k(k+1)\frac{1}{k(k + 1)} , that is, different elements in the sequence 12\frac12 , 16\frac{1}{6} , 112\frac{1}{12},.......
Back to ProblemsView on AoPS