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Omni-MATH / Let a₀, a₁, a₂, ... be an infinite sequence of real numbers satisfying the equation a_(n)=|a_(n+1)−a_(n+2)| for all n≥0, where a₀ and a₁ are two different positive reals. Can this …

Problem

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problem

Let a0a_0, a1a_1, a2a_2, ... be an infinite sequence of real numbers satisfying the equation an=|an+1−an+2|a_n=\left|a_{n+1}-a_{n+2}\right| for all n≥0n\geq 0, where a0a_0 and a1a_1 are two different positive reals. Can this sequence a0a_0, a1a_1, a2a_2, ... be bounded? [i]
Plain-text mathematical notation (without MathML)
Let a₀, a₁, a₂, ... be an infinite sequence of real numbers satisfying the equation a_(n)=|a_(n+1)−a_(n+2)| for all n≥0, where a₀ and a₁ are two different positive reals.

Can this sequence a₀, a₁, a₂, ... be bounded?

[i]
Original LaTeX notation
Let $a_0$, $a_1$, $a_2$, ... be an infinite sequence of real numbers satisfying the equation $a_n=\left|a_{n+1}-a_{n+2}\right|$ for all $n\geq 0$, where $a_0$ and $a_1$ are two different positive reals.

Can this sequence $a_0$, $a_1$, $a_2$, ... be bounded?

[i]

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Source and history

task_id
f00aeaf3-92e6-548e-bebc-ec4560776980
task_key
test--f00aeaf3-92e6-548e-bebc-ec4560776980
task_revision_id
1
config / split
/ test

Official source

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