lean_workbook_plus_76017

Proved

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

Prove that $\frac{1}{\sqrt{k}+\sqrt{k+1}} = \sqrt{k+1}-\sqrt{k}$ .

Preamble

import Mathlib.Analysis.Complex.Basic

Formal statement

theorem lean_workbook_plus_76017 : ∀ k : ℝ, k > 0 → 1 / (Real.sqrt k + Real.sqrt (k + 1)) = Real.sqrt (k + 1) - Real.sqrt k   :=  by sorry

Source