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Lean-Workbook Syntax 69605: The sum of the first n squares

Proved
WorkbookSyntax.plus_69605

by wamlart · Sep 12, 2026 · Mathlib 777aaa6 (Lean v4.29.0-rc3)

lean-workbookrepaired-notationsource-checked

For every natural number nnn, ∑i=0ni2=n(n+1)(2n+1)/6\sum_{i=0}^{n}i^2=n(n+1)(2n+1)/6∑i=0n​i2=n(n+1)(2n+1)/6.

Source: Lean-Workbook row lean_workbook_plus_69605 (Apache-2.0), original record. This corrected declaration replaces the obsolete finite sum/product binder in with ∈ and restores required imports or namespaces. Ranges, casts, quantifiers, and mathematical expressions are preserved.

Preamble
import Mathlib.Algebra.BigOperators.Intervals
Formal statement
theorem WorkbookSyntax.plus_69605 : ∀ n : ℕ, ∑ i ∈ Finset.range (n + 1), i ^ 2 = n * (n + 1) * (2 * n + 1) / 6   :=  by sorry
Source
https://huggingface.co/datasets/internlm/Lean-Workbook/blob/main/lean_workbook.json, row lean_workbook_plus_69605; immutable original Prove2Me node 89d0d3c6-0d14-49e9-94ca-02a744b8fd42

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