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Omni-MATH / Let a₀,a₁,a₂,… denote the sequence of real numbers such that a₀=2 and a_(n+1)=(a_(n))/(1+a_(n)) for n≥0. Compute a₂₀₁₂.

Problem

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problem

Let a0,a1,a2,…a_{0}, a_{1}, a_{2}, \ldots denote the sequence of real numbers such that a0=2a_{0}=2 and an+1=an1+ana_{n+1}=\frac{a_{n}}{1+a_{n}} for n≥0n \geq 0. Compute a2012a_{2012}.
Plain-text mathematical notation (without MathML)
Let a₀,a₁,a₂,… denote the sequence of real numbers such that a₀=2 and a_(n+1)=(a_(n))/(1+a_(n)) for n≥0. Compute a₂₀₁₂.
Original LaTeX notation
Let $a_{0}, a_{1}, a_{2}, \ldots$ denote the sequence of real numbers such that $a_{0}=2$ and $a_{n+1}=\frac{a_{n}}{1+a_{n}}$ for $n \geq 0$. Compute $a_{2012}$.

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Source and history

task_id
4354bccf-42bd-52c0-8652-e227a41dec83
task_key
test--4354bccf-42bd-52c0-8652-e227a41dec83
task_revision_id
1
config / split
/ test

Official source

initial import