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Omni-MATH / The Fibonacci numbers are defined by F₁=F₂=1 and F_(n+2)=F_(n+1)+F_(n) for n≥1. The Lucas numbers are defined by L₁=1,L₂=2, and L_(n+2)=L_(n+1)+L_(n) for n≥1. Calculate …

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problem

The Fibonacci numbers are defined by F1=F2=1F_{1}=F_{2}=1 and Fn+2=Fn+1+FnF_{n+2}=F_{n+1}+F_{n} for n≥1n \geq 1. The Lucas numbers are defined by L1=1,L2=2L_{1}=1, L_{2}=2, and Ln+2=Ln+1+LnL_{n+2}=L_{n+1}+L_{n} for n≥1n \geq 1. Calculate ∏n=115F2nFn∏n=113Ln\frac{\prod_{n=1}^{15} \frac{F_{2 n}}{F_{n}}}{\prod_{n=1}^{13} L_{n}}.
Plain-text mathematical notation (without MathML)
The Fibonacci numbers are defined by F₁=F₂=1 and F_(n+2)=F_(n+1)+F_(n) for n≥1. The Lucas numbers are defined by L₁=1,L₂=2, and L_(n+2)=L_(n+1)+L_(n) for n≥1. Calculate (∏_(n=1)¹⁵(F_(2n))/(F_(n)))/(∏_(n=1)¹³L_(n)).
Original LaTeX notation
The Fibonacci numbers are defined by $F_{1}=F_{2}=1$ and $F_{n+2}=F_{n+1}+F_{n}$ for $n \geq 1$. The Lucas numbers are defined by $L_{1}=1, L_{2}=2$, and $L_{n+2}=L_{n+1}+L_{n}$ for $n \geq 1$. Calculate $\frac{\prod_{n=1}^{15} \frac{F_{2 n}}{F_{n}}}{\prod_{n=1}^{13} L_{n}}$.

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Source and history

task_id
a83530ec-947f-5d9b-a4c3-cb8c40c466fe
task_key
test--a83530ec-947f-5d9b-a4c3-cb8c40c466fe
task_revision_id
1
config / split
/ test

Official source

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