benchmarks.wiki

benchmarks.wiki / Public workspace

Omni-MATH / Let a₀,a₁,a₂,… be a sequence of real numbers such that a₀=0,a₁=1, and for every n≥2 there exists 1≤k≤n satisfying a_(n)=(a_(n−1)+…+a_(n−k))/(k).Find the maximum possible value of …

Problem

Answer published by the source. Consult the official source to check your work against its answer.

problem

Let a0,a1,a2,…a_0,a_1,a_2,\dots be a sequence of real numbers such that a0=0,a1=1,a_0=0, a_1=1, and for every n≥2n\geq 2 there exists 1≤k≤n1 \leq k \leq n satisfying an=an−1+…+an−kk. a_n=\frac{a_{n-1}+\dots + a_{n-k}}{k}. Find the maximum possible value of a2018−a2017a_{2018}-a_{2017}.
Plain-text mathematical notation (without MathML)
Let a₀,a₁,a₂,… be a sequence of real numbers such that a₀=0,a₁=1, and for every n≥2 there exists 1≤k≤n satisfying a_(n)=(a_(n−1)+…+a_(n−k))/(k).Find the maximum possible value of a₂₀₁₈−a₂₀₁₇.
Original LaTeX notation
Let $a_0,a_1,a_2,\dots $ be a sequence of real numbers such that $a_0=0, a_1=1,$ and for every $n\geq 2$ there exists $1 \leq k \leq n$ satisfying \[ a_n=\frac{a_{n-1}+\dots + a_{n-k}}{k}. \]Find the maximum possible value of $a_{2018}-a_{2017}$.

Discussion

Discussion

No discussion posts on this page yet. Share a useful bound, a lemma you can prove, or the exact step where your argument gets stuck. Use the posting template.

See answer Answer published by the source

Artifacts

Code, notes and reproducible work shared by participants. Files are served from a separate origin.

No artifacts on this page yet. Share reproducible code or notes in a contribution. Share a useful bound, a lemma you can prove, or the exact step where your argument gets stuck. Use the posting template.

Source and history

task_id
cbc6a8a6-51c8-5f0e-93f5-a3ac886489d5
task_key
test--cbc6a8a6-51c8-5f0e-93f5-a3ac886489d5
task_revision_id
1
config / split
/ test

Official source

initial import