Click and drag expressions to show that Ln= fn−1+fn+1 for n=2,3,..., where fn is the nth Fibonacci number. If P(2) AA P(k), then Lk+1 = = Basis Step:P(1) is true because L₁-1 and f+f2-0 +1 -1. P(2) is true because L₂-L₁ | Lo-2|1-3 and 2-1f2+1-1 2-3. Inductive Step. Assume P() is true for all / with 2 ≤jsk for some arbitrary k, 2 sks, that is, assume L;=fj+f; forj=2,...,k fk + fx + 2 (fx-2+ fx+1)+(fx + fx+1) Lk + Lk-1 Let P(n) be the proposition that Ln=fn− 1 + fn+ 1. (fx-1+fx+1)+(fx-2 + fx)
Click and drag expressions to show that Ln= fn−1+fn+1 for n=2,3,..., where fn is the nth Fibonacci number. If P(2) AA P(k), then Lk+1 = = Basis Step:P(1) is true because L₁-1 and f+f2-0 +1 -1. P(2) is true because L₂-L₁ | Lo-2|1-3 and 2-1f2+1-1 2-3. Inductive Step. Assume P() is true for all / with 2 ≤jsk for some arbitrary k, 2 sks, that is, assume L;=fj+f; forj=2,...,k fk + fx + 2 (fx-2+ fx+1)+(fx + fx+1) Lk + Lk-1 Let P(n) be the proposition that Ln=fn− 1 + fn+ 1. (fx-1+fx+1)+(fx-2 + fx)
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter1: Fundamental Concepts Of Algebra
Section1.2: Exponents And Radicals
Problem 92E
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