Sum of integers below 401

Proved

FiniteTriangular.sum_range_401

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

arithmeticfinite-sum

The sum of the nonnegative integers strictly less than $401$ equals $80200$ . Equivalently, $\\sum_{k=0}^{401-1} k = 401(401-1)/2$ .

Preamble

import Mathlib
open Finset

Formal statement

namespace FiniteTriangular

theorem sum_range_401 : ∑ k ∈ range 401, k = 80200 := 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.