MathDB
IMC2015, problem 3

Source: IMC2015

July 29, 2015
Sequencesseriescollege contestsIMC2015

Problem Statement

Let F(0)=0F(0)=0, F(1)=32F(1)=\frac32, and F(n)=52F(n−1)−F(n−2)F(n)=\frac{5}{2}F(n-1)-F(n-2) for n≥2n\ge2.
Determine whether or not ∑n=0∞ 1F(2n)\displaystyle{\sum_{n=0}^{\infty}\, \frac{1}{F(2^n)}} is a rational number.
(Proposed by Gerhard Woeginger, Eindhoven University of Technology)
Back to ProblemsView on AoPS