Sum of integers below 408

Proved

FiniteTriangular.sum_range_408

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

arithmeticfinite-sum

The sum of the nonnegative integers strictly less than $408$ equals $83028$ . Equivalently, $\\sum_{k=0}^{408-1} k = 408(408-1)/2$ .

Preamble

import Mathlib
open Finset

Formal statement

namespace FiniteTriangular

theorem sum_range_408 : ∑ k ∈ range 408, k = 83028 := 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.