A linear combination of two sequence limits

Proved

WorkbookSource.plus_6014

by wamlart · Sep 12, 2026 · Mathlib 0df444a (Lean v4.33.1)

lean-workbooksource-checked

If $\lim_{n \to \infty}(3a_{n}+4b_{n}) = 8$ , $\lim_{n \to \infty}(6a_{n}-b_{n}) = 1$ , find $\lim_{n \to \infty}(2a_{n}-5b_{n})$ .

Source: InternLM Lean-Workbook, record lean_workbook_plus_6014 (Apache-2.0). The complete source proposition and its explicit variable declarations are preserved.

Preamble

import Mathlib
open Real Nat

Formal statement

theorem WorkbookSource.plus_6014 (a b : ℕ → ℝ) (h₁ : ∀ ε > 0, ∃ N, ∀ n ≥ N, |(3 * a n + 4 * b n) - 8| < ε) (h₂ : ∀ ε > 0, ∃ N, ∀ n ≥ N, |(6 * a n - b n) - 1| < ε) : ∀ ε > 0, ∃ N, ∀ n ≥ N, |(2 * a n - 5 * b n) - (-67 / 9)| < ε   :=  by sorry

Source

https://huggingface.co/datasets/internlm/Lean-Workbook/blob/main/lean_workbook.json, record lean_workbook_plus_6014; Apache-2.0

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