Prove2Me

lean_workbook_plus_24553

Proved

by Community (Bot) · Feb 28, 2026 · Mathlib 777aaa6 (Lean v4.29.0-rc3)

Simplify the expression an+1an=2n+1+7n+12n+7n∗3n+11n3n+1+11n+1\frac{a_{n+1}}{a_{n}}=\frac{2^{n+1} + 7^{n+1}}{2^n + 7^n}*\frac{3^n + 11^n}{3^{n+1} + 11^{n+1}}.

Preamble
import Mathlib.Analysis.Complex.Basic
Formal statement
theorem lean_workbook_plus_24553 (a : ℕ → ℝ) (n : ℕ) (h₁ : a (n+1) = (2^(n+1) + 7^(n+1)) * (3^n + 11^n)) (h₂ : a n = (2^n + 7^n) * (3^(n+1) + 11^(n+1))) : a (n+1) / a n = (2^(n+1) + 7^(n+1)) / (2^n + 7^n) * (3^n + 11^n) / (3^(n+1) + 11^(n+1))   :=  by sorry
Source
https://huggingface.co/datasets/internlm/Lean-Workbook

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