benchmarks.wiki

benchmarks.wiki / Public workspace

Omni-MATH / Let p_(i) be the ith prime. Let f(x)=∑_(i=1)⁵⁰p_(i)x^(i−1)=2+3x+⋯+229x⁴⁹ If a is the unique positive real number with f(a)=100, estimate A=⌊100000a⌋. An estimate of E will earn …

Problem

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

problem

Let pip_{i} be the iith prime. Let f(x)=∑i=150pixi−1=2+3x+⋯+229x49f(x)=\sum_{i=1}^{50} p_{i} x^{i-1}=2+3x+\cdots+229x^{49} If aa is the unique positive real number with f(a)=100f(a)=100, estimate A=⌊100000a⌋A=\lfloor 100000a\rfloor. An estimate of EE will earn max(0,⌊20−|A−E|/250⌋)\max (0,\lfloor 20-|A-E| / 250\rfloor) points.
Plain-text mathematical notation (without MathML)
Let p_(i) be the ith prime. Let f(x)=∑_(i=1)⁵⁰p_(i)x^(i−1)=2+3x+⋯+229x⁴⁹ If a is the unique positive real number with f(a)=100, estimate A=⌊100000a⌋. An estimate of E will earn max(0,⌊20−|A−E|/250⌋) points.
Original LaTeX notation
Let $p_{i}$ be the $i$th prime. Let $$f(x)=\sum_{i=1}^{50} p_{i} x^{i-1}=2+3x+\cdots+229x^{49}$$ If $a$ is the unique positive real number with $f(a)=100$, estimate $A=\lfloor 100000a\rfloor$. An estimate of $E$ will earn $\max (0,\lfloor 20-|A-E| / 250\rfloor)$ points.

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
34cb41d1-4c9a-5f9c-a21e-4410c2210c42
task_key
test--34cb41d1-4c9a-5f9c-a21e-4410c2210c42
task_revision_id
1
config / split
/ test

Official source

initial import