Prove2Me

The alternating sum of a positive binomial row

Proved
WorkbookSource.problem_4767

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

lean-workbookrepaired-notationsource-checked

Prove that, (n0)−(n1)+(n2).......(−1)n(nn)=0\binom{n}{0}-\binom{n}{1}+\binom{n}{2}.......(-1)^n\binom{n}{n}=0 Where n>0

Source: InternLM Lean-Workbook, record lean_workbook_4767 (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_4767 (n : ℕ) (h : n > 0) : ∑ k ∈ Finset.range (n + 1), (-1 : ℤ)^k * choose n k = 0  :=  by sorry
Source
https://huggingface.co/datasets/internlm/Lean-Workbook/blob/main/lean_workbook.json, record lean_workbook_4767; Apache-2.0

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