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Omni-MATH / Let F(0)=0,F(1)=(3)/(2), and F(n)=(5)/(2)F(n−1)−F(n−2) for n≥2. Determine whether or not ∑_(n=0)^(∞)(1)/(F(2^(n))) is a rational number.

Problem

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problem

Let F(0)=0,F(1)=32F(0)=0, F(1)=\frac{3}{2}, and F(n)=52F(n−1)−F(n−2)F(n)=\frac{5}{2} F(n-1)-F(n-2) for n≥2n \geq 2. Determine whether or not ∑n=0∞1F(2n)\sum_{n=0}^{\infty} \frac{1}{F\left(2^{n}\right)} is a rational number.
Plain-text mathematical notation (without MathML)
Let F(0)=0,F(1)=(3)/(2), and F(n)=(5)/(2)F(n−1)−F(n−2) for n≥2. Determine whether or not ∑_(n=0)^(∞)(1)/(F(2^(n))) is a rational number.
Original LaTeX notation
Let $F(0)=0, F(1)=\frac{3}{2}$, and $F(n)=\frac{5}{2} F(n-1)-F(n-2)$ for $n \geq 2$. Determine whether or not $\sum_{n=0}^{\infty} \frac{1}{F\left(2^{n}\right)}$ is a rational number.

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Source and history

task_id
f6ca765c-0069-594d-b860-1062ebc4fe1e
task_key
test--f6ca765c-0069-594d-b860-1062ebc4fe1e
task_revision_id
1
config / split
/ test

Official source

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