We Will Investigate Some Properties Of The Fibonacci Numbers These Are Defined By F 1 F 1 And Fn Fn 1 Fn 2 1 (23.36 KiB) Viewed 27 times
The problem is to prove Corollary 1: For all n in the naturalnumbers
We will investigate some properties of the Fibonacci numbers. These are defined by F₁ = 1, F₂ = 1, and Fn = Fn-1 + Fn-2 for n ≥ 3. So the first few are given by 1, 1,2,3,5,8,.... Let a = 1+√5 and 3 = 1-5; these are the two roots of the polynomial x²-x-1=0. Corollary 1. For all n € N, F₁ is the closest integer to Hint: How big can |F₁-be? Proof.
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