lean_workbook_plus_28664

Proved

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

Using the close form of an infinite geometric series: $\sum_{n=1}^{\infty}ar^{n-1}=\frac{a}{1-r}$ where $a$ is the first term, and $r$ is the common ratio, we obtain $p=\frac{\frac{1}{2}}{1-\frac{1}{4}}=\frac{2}{3}$

Preamble

import Mathlib.Analysis.Complex.Basic

Formal statement

theorem lean_workbook_plus_28664  (a : ℝ)
  (h₀ : a = 1 / 2)
  (r : ℝ)
  (h₁ : r = 1 / 4) :
  a / (1 - r) = 2 / 3   :=  by sorry

Source

https://huggingface.co/datasets/internlm/Lean-Workbook

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