lean_workbook_plus_55038

Proved

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

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

Preamble

import Mathlib.Analysis.Complex.Basic

Formal statement

theorem lean_workbook_plus_55038 (n : ℕ) : 1 / (Real.sqrt n + Real.sqrt (n + 1)) = Real.sqrt (n + 1) - Real.sqrt n   :=  by sorry

Source