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MMLU-Pro / 8212 / For any poitie integer n, let ⟨n⟩ denote the closest integer to…

Problem

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

question

For any poitie integer nn, let ⟨n⟩\langle n\rangle denote the closest integer to n\sqrt{n}. Evaluate ∑n=1∞2⟨n⟩+2−⟨n⟩2n\sum_{n=1}^{\infty} \frac{2^{\langle n \rangle}+2^{-\langle n \rangle}}{2^n}.
Plain-text mathematical notation (without MathML)
For any poitie integer n, let ⟨n⟩ denote the closest integer to √(n). Evaluate ∑_(n=1)^(∞)(2^(⟨n⟩)+2^(−⟨n⟩))/(2^(n)).
Original LaTeX notation
For any poitie integer $n$, let $\langle n\rangle$ denote the closest integer to $\sqrt{n}$. Evaluate $\sum_{n=1}^{\infty} \frac{2^{\langle n \rangle}+2^{-\langle n \rangle}}{2^n}$.

category

math

options

  1. 7.0
  2. 2.0
  3. 4.5
  4. 1.0
  5. 5.0
  6. 6.0
  7. 4.0
  8. 2.5
  9. 3.0
  10. 8.0

src

theoremQA-Math

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Source and history

upstream_id / Original problem ID
8212
task_id
e4ad2828-6b65-5411-b497-7bd9d69574a7
task_key
default--test--8212
task_revision_id
1
config / split
default / test

Official source

initial import