lean_workbook_plus_44974

Proved

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

Prove that $n+\frac{1}{2}<\sqrt{n^2+n+1}<n+1$ for all positive integers n.

Preamble

import Mathlib.Analysis.Complex.Basic

Formal statement

theorem lean_workbook_plus_44974 (n : ℕ) (hn : n > 0) : (n + 1/2) < Real.sqrt (n^2 + n + 1) ∧ Real.sqrt (n^2 + n + 1) < n + 1   :=  by sorry

Source