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MMLU-Pro / 7756 / Does the following series ∑_(i=0)^(∞)(n!)/(n²cos(n)) converge?

Problem

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

question

Does the following series ∑i=0∞n!n2cos(n)\sum_{i=0}^{\infty} \frac{n!}{n^2 cos(n)} converge?
Plain-text mathematical notation (without MathML)
Does the following series ∑_(i=0)^(∞)(n!)/(n²cos(n)) converge?
Original LaTeX notation
Does the following series $\sum_{i=0}^{\infty} \frac{n!}{n^2 cos(n)}$ converge?

category

math

options

  1. Converges to $e$ (Euler's number)
  2. 1.0
  3. Converges to $\pi$
  4. Diverges
  5. Converges absolutely
  6. It's a constant series
  7. Converges conditionally
  8. 0.0
  9. Diverges to infinity
  10. Alternates between positive and negative values

src

theoremQA-Math

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Source and history

upstream_id / Original problem ID
7756
task_id
46b22222-cdac-568c-b807-78da02a3a181
task_key
default--test--7756
task_revision_id
1
config / split
default / test

Official source

initial import