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MMLU-Pro / 7968 / suppose the sequence a_n satisfies 0<a_n<1, and (1−a_(n))a_(n+1)>1/4 for all n,…

Problem

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

question

suppose the sequence a_n satisfies 0<a_n<1, and (1−an)an+1>1/4(1-a_n)a_{n+1}>1/4 for all n, what is the limit of a_n as n goes to infinity?
Plain-text mathematical notation (without MathML)
suppose the sequence a_n satisfies 0<a_n<1, and (1−a_(n))a_(n+1)>1/4 for all n, what is the limit of a_n as n goes to infinity?
Original LaTeX notation
suppose the sequence a_n satisfies 0<a_n<1, and $(1-a_n)a_{n+1}>1/4$ for all n, what is the limit of a_n as n goes to infinity?

category

math

options

  1. 0.33
  2. 0.75
  3. 0.5
  4. 0.25
  5. 2/3
  6. The sequence does not converge
  7. 1/n as n goes to infinity
  8. 0.6
  9. 0.8
  10. 1

src

theoremQA-Math

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Source and history

upstream_id / Original problem ID
7968
task_id
b925f822-b2e0-5b7a-85fc-f430f7f0b2de
task_key
default--test--7968
task_revision_id
1
config / split
default / test

Official source

initial import