International Mathematics Competition
for University Students
2015

IMC2015: Day 1, Problem 3

3. Let $F(0)=0$, $F(1)=\frac32$, and $F(n)=\frac{5}{2}F(n-1)-F(n-2)$ for $n\ge2$.

Determine whether or not $\displaystyle{\sum_{n=0}^{\infty}\, \frac{1}{F(2^n)}}$ is a rational number.

Proposed by Gerhard Woeginger, Eindhoven University of Technology

  Hint    Solution