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MMLU-Pro / 8214 / suppose sequence x_n satisfies x_n*x_n+1=n for all n>=1, and…

Problem

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

question

suppose sequence x_n satisfies x_n*x_{n+1}=n for all n>=1, and limn→∞xnxn+1=1\lim_{n\rightarrow\infty}\frac{x_n}{x_{n+1}}=1. What's the value of $\pi*x_1^2$?
Plain-text mathematical notation (without MathML)
suppose sequence x_n satisfies x_n*x_{n+1}=n for all n>=1, and lim_(n→∞)(x_(n))/(x_(n+1))=1. What's the value of $\pi*x_1^2$?
Original LaTeX notation
suppose sequence x_n satisfies x_n*x_{n+1}=n for all n>=1, and $\lim_{n\rightarrow\infty}\frac{x_n}{x_{n+1}}=1$. What's the value of $\pi*x_1^2$?

category

math

options

  1. 3.14
  2. 2.0
  3. 4.0
  4. 2.5
  5. 6.0
  6. 5.0
  7. 0.5
  8. 1.0
  9. 3.5
  10. 3.0

src

theoremQA-Math

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Source and history

upstream_id / Original problem ID
8214
task_id
ec6b5c0f-8fbb-5535-8c4c-db1263b70aef
task_key
default--test--8214
task_revision_id
1
config / split
default / test

Official source

initial import