## 2015 IMC Day 1 Problem 3

2015 IMC 1.3. Let $F(0) = 0$, $F(1) = \frac{3}{2}$, and $F(n) = \frac{5}{2}F(n-1) - F(n-2)$ for $n \leq 2$.

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