--- /dev/null +++ b/Mathlib/Unsorry/SumRangePowFourClosedForm.lean @@ -0,0 +1,15 @@ +/- +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 +import Mathlib.Tactic.Ring + +theorem sum_range_pow_four_closed (n : ℕ) : 30 * (∑ k ∈ Finset.range (n + 1), (k : ℤ) ^ 4) = n * (n + 1) * (2 * n + 1) * (3 * n ^ 2 + 3 * n - 1) := by + induction n with + | zero => simp + | succ n ih => + rw [Finset.sum_range_succ, mul_add, ih] + push_cast + ring