Let Fn denote the Fibonnaci sequence defined by Fn = F(n-1) + F(n-2) for n >= 2 with initial values FO=F1=1. Using Mathematical Induction prove that the identity %3D Fn² – F(n – 1) · F(n+1) = (–1)" - holds for alln >= 1

Let Fn denote the Fibonnaci sequence defined by Fn = F(n-1) + F(n-2) for n >= 2 with initial values FO=F1=1. Using Mathematical Induction prove that the identity %3D Fn² – F(n – 1) · F(n+1) = (–1)" - holds for alln >= 1

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Differential Equations

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Question

Let Fn denote the Fibonnaci sequence
defined by
Fn = F(n-1) + F(n-2)
for n >= 2 with initial values FO=F1=1. Using
Mathematical Induction prove that the
identity
%3D
Fn² – F (n – 1) · F(n+1) = (-1)"
holds for alln >= 1

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