Sum of the nonnegative integers below 1016

Proved

FiniteTriangular.sum_range_1016

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

algebrafinset

The sum of the integers from $0$ through $1015$ equals $515620$ , which is the triangular number $\\frac{1016(1015)}{2}$ .

Preamble

import Mathlib
open Finset

Formal statement

namespace FiniteTriangular
theorem sum_range_1016 : ∑ k ∈ range 1016, k = 515620 := by sorry
end FiniteTriangular

Source

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