lean_workbook_plus_14179

Proved

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

The closed form for this is $a_n=\frac{1}{2\sqrt{2}} \left((1+\sqrt 2)^n-(1-\sqrt 2 )^n \right)$

Preamble

import Mathlib.Analysis.Complex.Basic

Formal statement

theorem lean_workbook_plus_14179 (n : ℕ) : ∃ a : ℝ, a = (1 / (2 * Real.sqrt 2)) * ((1 + Real.sqrt 2)^n - (1 - Real.sqrt 2)^n)   :=  by sorry

Source