lean_workbook_plus_11132

Proved

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

prove that: for $k>1$ , $\frac{1}{\sqrt{k}+\sqrt{k-1}}<\frac{1}{\sqrt{k}}$

Preamble

import Mathlib.Analysis.Complex.Basic

Formal statement

theorem lean_workbook_plus_11132 (k : ℕ) (h : 1 < k) : (1:ℝ) / (Real.sqrt k + Real.sqrt (k - 1)) < (1:ℝ) / Real.sqrt k   :=  by sorry

Source