Sum of the nonnegative integers below 1013

Proved

FiniteTriangular.sum_range_1013

by carlok · Sep 26, 2026 · Mathlib 0df444a (Lean v4.33.1)

algebrafinset

The sum of the integers from $0$ through $1012$ equals $512578$ , which is the triangular number $\\frac{1013(1012)}{2}$ .

Preamble

import Mathlib
open Finset

Formal statement

namespace FiniteTriangular
theorem sum_range_1013 : ∑ k ∈ range 1013, k = 512578 := by sorry
end FiniteTriangular

Source

The closed form for the sum of an initial segment of the nonnegative integers.