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Omni-MATH / We say that a sequence a₁,a₂,⋯ is [i]expansive[/i] if for all positive integers j, i<j implies |a_(i)−a_(j)|≥(1)/(j). Find all positive real numbers C for which one can find an exp…

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problem

We say that a sequence a1,a2,⋯a_1,a_2,\cdots is [i]expansive[/i] if for all positive integers j,i<jj,\; i<j implies |ai−aj|≥1j|a_i-a_j|\ge \tfrac 1j. Find all positive real numbers CC for which one can find an expansive sequence in the interval [0,C][0,C].
Plain-text mathematical notation (without MathML)
We say that a sequence a₁,a₂,⋯ is [i]expansive[/i] if for all positive integers j, i<j implies |a_(i)−a_(j)|≥(1)/(j). Find all positive real numbers C for which one can find an expansive sequence in the interval [0,C].
Original LaTeX notation
We say that a sequence $a_1,a_2,\cdots$ is [i]expansive[/i] if for all positive integers $j,\; i<j$ implies $|a_i-a_j|\ge \tfrac 1j$. Find all positive real numbers $C$ for which one can find an expansive sequence in the interval $[0,C]$.

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task_id
5b11c8da-a872-51dd-be81-bc5d59a4f8cd
task_key
test--5b11c8da-a872-51dd-be81-bc5d59a4f8cd
task_revision_id
1
config / split
/ test

Official source

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