Sum of integers below 416

Proved

FiniteTriangular.sum_range_416

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

arithmeticfinite-sum

The sum of the nonnegative integers strictly less than $416$ equals $86320$ . Equivalently, $\\sum_{k=0}^{416-1} k = 416(416-1)/2$ .

Preamble

import Mathlib
open Finset

Formal statement

namespace FiniteTriangular

theorem sum_range_416 : ∑ k ∈ range 416, k = 86320 := 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.