An exact geometric-series sum

Proved

WorkbookSource.problem_21029

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

lean-workbookrepaired-notationsource-checked

Calculate the sum of the geometric series with $a_1 = 4096$ , $r = -\frac{1}{2}$ , and $n = 16$ .

Source: InternLM Lean-Workbook, record lean_workbook_21029 (Apache-2.0). The complete source proposition and its explicit variable declarations are preserved. Notation repair: Replaced legacy ∑ i in s binder notation with current ∑ i ∈ s; no binder/domain/proposition change.

Preamble

import Mathlib
open Real Nat

Formal statement

theorem WorkbookSource.problem_21029 (a : ℕ) (r : ℚ) (n : ℕ) (h₁ : a = 4096) (h₂ : r = -1/2) (h₃ : n = 16) : ∑ i ∈ Finset.range n, a * r^i = 2730.625  :=  by sorry

Source

https://huggingface.co/datasets/internlm/Lean-Workbook/blob/main/lean_workbook.json, record lean_workbook_21029; Apache-2.0

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