lean_workbook_plus_21771

Proved

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

Derivation of the identity: $ \left(\frac{n}{\sqrt{n(n+1)}}\right)^2+\left(\frac{1}{\sqrt{n+1}}\right)^2=1 $

Preamble

import Mathlib.Analysis.Complex.Basic

Formal statement

theorem lean_workbook_plus_21771 (n : ℕ) (hn : n ≠ 0) : ((n:ℝ) / √(n * (n + 1)))^2 + (1 / √(n + 1))^2 = 1   :=  by sorry

Source