The closed form of a halving recurrence

Proved

WorkbookSource.problem_39600

by wamlart · Sep 12, 2026 · Mathlib 0df444a (Lean v4.33.1)

lean-workbooksource-checked

Prove by induction that $y_n=\frac{3}{2^{n+1}}$ .

Source: InternLM Lean-Workbook, record lean_workbook_39600 (Apache-2.0). The complete source proposition and explicit variable declarations are preserved.

Preamble

import Mathlib
open Real Nat

Formal statement

theorem WorkbookSource.problem_39600 (y : ℕ → ℝ) (n : ℕ) (h₁ : y 0 = 3/2) (h₂ : ∀ n, y (n+1) = (y n)/2) : y n = 3 / 2 ^ (n + 1)  :=  by sorry

Source

https://huggingface.co/datasets/internlm/Lean-Workbook/blob/main/lean_workbook.json, record lean_workbook_39600; Apache-2.0

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