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

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Finally We Will Investigate Some Properties Of The Fibonacci Numbers These Are Defined By F 1 F 1 And Fnfn 1 1 (33.29 KiB) Viewed 53 times

Finally, we will investigate some properties of the Fibonacci numbers. These are defined by F₁ = 1, F₂ = 1, and FnFn-1 + Fn-2 for n ≥ 3. So the first few are given by 1, 1, 2, 3, 5, 8,... two roots of the polynomial 2²-2-1=0. Theorem 2. For all ne N we have Fn = Proof. Hint: this should involve no unpleasant algebra. Use the polynomial. Corollary 1. For all neN, Fn is the closest integer to Proof. Hint: How big can Fn- Fn-be? Let a = 1+5 and 3= 15; these are the G"-8" 0 0