Finally, we will investigate some properties of the Fibonacci numbers. These are defined by F₁ = 1, F₂ = 1, and Fn = Fn-

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Finally We Will Investigate Some Properties Of The Fibonacci Numbers These Are Defined By F 1 F 1 And Fn Fn 1 (24.81 KiB) Viewed 39 times

Finally, 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-√³; these are the two roots of the polynomial x²-x-1=0. Theorem 2: For all n € N we have F₁ = ²-3² Hint: This should involve no unpleasant algebra. Use the polynomial. Proof.