lean_workbook_plus_60873

Proved

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

Prove that $(1+x)^n \ge 1+nx$ for all natural numbers $n$ , if you are given that $x>-1$ .

Preamble

import Mathlib.Analysis.Complex.Basic

Formal statement

theorem lean_workbook_plus_60873 (n : ℕ) (x : ℝ) (hx : x > -1) : (1 + x) ^ n ≥ 1 + n * x   :=  by sorry

Source