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MATH / The first two terms of a sequence are a₁=1 and a₂=(1)/(√(3)). For n≥1, …a₂₀₀₉?

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problem

The first two terms of a sequence are a1=1a_1 = 1 and a2=13a_2 = \frac {1}{\sqrt3}. For n≥1n\ge1, \begin{align*} a_{n + 2} = \frac {a_n + a_{n + 1}}{1 - a_na_{n + 1}}. \end{align*}What is a2009a_{2009}?
Plain-text mathematical notation (without MathML)
The first two terms of a sequence are a₁=1 and a₂=(1)/(√(3)). For n≥1, \begin{align*} a_{n + 2} = \frac {a_n + a_{n + 1}}{1 - a_na_{n + 1}}. \end{align*}What is a₂₀₀₉?
Original LaTeX notation
The first two terms of a sequence are $a_1 = 1$ and $a_2 = \frac {1}{\sqrt3}$. For $n\ge1$, \begin{align*} a_{n + 2} = \frac {a_n + a_{n + 1}}{1 - a_na_{n + 1}}. \end{align*}What is $a_{2009}$?

level

Level 3

type

Precalculus

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Source and history

task_id
b7d6126c-2e3d-5955-929c-1fe8ebee1f3f
task_key
precalculus--test--b7d6126c-2e3d-5955-929c-1fe8ebee1f3f
task_revision_id
1
config / split
precalculus / test

Official source

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