lean_workbook_plus_34548

Proved

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

Prove that $\frac{1}{k^3}<\frac{1}{2}\left( \frac{1}{(k-1)^2}-\frac{1}{k^2} \right)$

Preamble

import Mathlib.Analysis.Complex.Basic

Formal statement

theorem lean_workbook_plus_34548  (k : ℕ) (hk : 1 < k) :
  (1 : ℝ) / k^3 < 1 / 2 * (1 / (k - 1)^2 - 1 / k^2)   :=  by sorry

Source