The Fibonacci numbers are defined by the sequence and for F₁ = 1, F₂ = 1 and Fn = Fn-1 + Fn-2 n> 3 The Lucas numbers are

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The Fibonacci Numbers Are Defined By The Sequence And For F 1 F 1 And Fn Fn 1 Fn 2 N 3 The Lucas Numbers Are 1 (42.95 KiB) Viewed 72 times

The Fibonacci numbers are defined by the sequence and for F₁ = 1, F₂ = 1 and Fn = Fn-1 + Fn-2 n> 3 The Lucas numbers are defined similarly (the same recursive sequence, but different starting points) L₁ = 1, L₂ = 3 Ln = Ln−1 + Ln-2 for n ≥ 3 Use induction (weak or strong, as appropriate) to prove that Ln = Fn + 2Fn–1 for n ≥ 2.