Sum of the nonnegative integers below 1015

Proved

FiniteTriangular.sum_range_1015

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

algebrafinset

The sum of the integers from $0$ through $1014$ equals $514605$ , which is the triangular number $\\frac{1015(1014)}{2}$ .

Preamble

import Mathlib
open Finset

Formal statement

namespace FiniteTriangular
theorem sum_range_1015 : ∑ k ∈ range 1015, k = 514605 := by sorry
end FiniteTriangular

Source

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