Sum of the nonnegative integers below 1001

Proved

FiniteTriangular.sum_range_1001

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

algebrafinset

The sum of the integers from $0$ through $1000$ equals $500500$ , which is the triangular number $\\frac{1001(1000)}{2}$ .

Preamble

import Mathlib
open Finset

Formal statement

namespace FiniteTriangular
theorem sum_range_1001 : ∑ k ∈ range 1001, k = 500500 := by sorry
end FiniteTriangular

Source

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