Question 4 The Fibonacci numbers are defined by the sequence F₁ = 1, F₂2 = 1 and for Fn = Fn-1 + Fn-2 and n> 3 The Lucas

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Question 4 The Fibonacci Numbers Are Defined By The Sequence F 1 F 2 1 And For Fn Fn 1 Fn 2 And N 3 The Lucas 1 (55.56 KiB) Viewed 11 times

Question 4 The Fibonacci numbers are defined by the sequence F₁ = 1, F₂2 = 1 and for Fn = Fn-1 + Fn-2 and n> 3 The Lucas numbers are defined similarly (the same recursive sequence, but differer L₁ = 1, L2 = 3 Ln Ln-1+ Ln-2 for n ≥ 3 Use induction (weak or strong, as appropriate) to prove that In = = Fn+2Fn-1 for n ≥ 2.