--- /dev/null +++ b/Mathlib/Unsorry/NicomachusSumCubesTriangular.lean @@ -0,0 +1,10 @@ +/- +Copyright (c) 2026 Chris Barlow. All rights reserved. +Released under Apache 2.0 license as described in the file LICENSE. +Authors: Chris Barlow +-/ +import Mathlib.Algebra.BigOperators.Intervals + +theorem sum_range_cube_eq_triangular_sq (n : ℕ) : ∑ i ∈ Finset.range (n + 1), i ^ 3 = (n * (n + 1) / 2) ^ 2 := by + rw [nicomachus_sum_cubes (n + 1), Finset.sum_range_id, Nat.add_sub_cancel, + Nat.mul_comm (n + 1) n]