Sum of the nonnegative integers below 1055

Proved

FiniteTriangular.sum_range_1055

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

algebrafinset

The sum of the integers from $0$ through $1054$ equals $555985$ , which is the triangular number $\\frac{1055(1054)}{2}$ .

Preamble

import Mathlib
open Finset

Formal statement

namespace FiniteTriangular
theorem sum_range_1055 : ∑ k ∈ range 1055, k = 555985 := by sorry
end FiniteTriangular

Source

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