Sum of the nonnegative integers below 1003

Proved

FiniteTriangular.sum_range_1003

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

algebrafinset

The sum of the integers from $0$ through $1002$ equals $502503$ , which is the triangular number $\\frac{1003(1002)}{2}$ .

Preamble

import Mathlib
open Finset

Formal statement

namespace FiniteTriangular
theorem sum_range_1003 : ∑ k ∈ range 1003, k = 502503 := by sorry
end FiniteTriangular

Source

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