benchmarks.wiki

benchmarks.wiki / Public workspace

MATH / Let a₁, a₂, … be a sequence of real numbers such that for all positive integers n, ∑_(k=1)^(n)a_(k)((k)/(n))²=1.Find the smallest n such that a_(n)<(1)/(2018).

Problem

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

problem

Let a1,a_1, a2,a_2, …\dots be a sequence of real numbers such that for all positive integers n,n, ∑k=1nak(kn)2=1.\sum_{k = 1}^n a_k \left( \frac{k}{n} \right)^2 = 1.Find the smallest nn such that an<12018.a_n < \frac{1}{2018}.
Plain-text mathematical notation (without MathML)
Let a₁, a₂, … be a sequence of real numbers such that for all positive integers n,
∑_(k=1)^(n)a_(k)((k)/(n))²=1.Find the smallest n such that a_(n)<(1)/(2018).
Original LaTeX notation
Let $a_1,$ $a_2,$ $\dots$ be a sequence of real numbers such that for all positive integers $n,$
\[\sum_{k = 1}^n a_k \left( \frac{k}{n} \right)^2 = 1.\]Find the smallest $n$ such that $a_n < \frac{1}{2018}.$

level

Level 5

type

Intermediate Algebra

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
2bc4a236-be87-5f59-9400-af3aa5e6a362
task_key
intermediate~5falgebra--test--2bc4a236-be87-5f59-9400-af3aa5e6a362
task_revision_id
1
config / split
intermediate_algebra / test

Official source

initial import