--- /dev/null +++ b/Mathlib/Unsorry/SumRangeFibSq.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.Group.Finset.Basic +import Mathlib.Data.Nat.Fib.Basic +import Mathlib.Tactic.Ring + +theorem sum_range_succ_fib_sq (n : ℕ) : ∑ i ∈ Finset.range (n + 1), Nat.fib i ^ 2 = Nat.fib n * Nat.fib (n + 1) := by + induction n with + | zero => simp + | succ k ih => + rw [Finset.sum_range_succ, ih, Nat.fib_add_two] + ring