--- /dev/null +++ b/Mathlib/Unsorry/SumRangeSqClosedForm.lean @@ -0,0 +1,14 @@ +/- +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.Group.Finset.Basic +import Mathlib.Tactic.Ring + +theorem sum_range_sq_closed_form (n : ℕ) : 6 * ∑ i ∈ Finset.range (n + 1), i ^ 2 = n * (n + 1) * (2 * n + 1) := by + induction n with + | zero => simp + | succ k ih => + rw [Finset.sum_range_succ, mul_add, ih] + ring