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.

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