Sum of integers below 685

Proved

FiniteTriangular.sum_range_685

by carlok · Sep 25, 2026 · Mathlib 0df444a (Lean v4.33.1)

arithmeticfinite-sum

The sum of the nonnegative integers strictly less than $685$ equals $234270$ . Equivalently, $\\sum_{k=0}^{685-1} k = 685(685-1)/2$ .

Preamble

import Mathlib
open Finset

Formal statement

namespace FiniteTriangular

theorem sum_range_685 : ∑ k ∈ range 685, k = 234270 := by sorry

end FiniteTriangular

Source

Elementary arithmetic series: the sum of the first m positive integers is m(m+1)/2, rewritten on Finset.range.