lean_workbook_plus_40511

Proved

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

For positive real numbers $a,b$ and positive integers $n$ , prove that $\frac{1}{na+b}+\frac{1}{a+nb} \leq \frac{1}{n+1}(\frac{1}{a} + \frac{1}{b}).$

Preamble

import Mathlib.Analysis.Complex.Basic

Formal statement

theorem lean_workbook_plus_40511 (a b : ℝ) (n : ℕ) (ha : 0 < a) (hb : 0 < b) : (1 / (n * a + b) + 1 / (a + n * b)) ≤ (1 / (n + 1) * (1 / a + 1 / b))   :=  by sorry

Source

https://huggingface.co/datasets/internlm/Lean-Workbook

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