Sum of the nonnegative integers below 1010

Proved

FiniteTriangular.sum_range_1010

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

algebrafinset

The sum of the integers from $0$ through $1009$ equals $509545$ , which is the triangular number $\\frac{1010(1009)}{2}$ .

Preamble

import Mathlib
open Finset

Formal statement

namespace FiniteTriangular
theorem sum_range_1010 : ∑ k ∈ range 1010, k = 509545 := by sorry
end FiniteTriangular

Source

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