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IMC2015: Day 1, Problem 33. 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: Express $F(n)$ in terms of $n$. The sum of the series has a nice form. | |||||||||
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