2) Using induction on n, prove for all positive integers n that: [F2n + 1 F2n F2n - F2n – 1 where Fn denotes the nth Fibonacci number.

Elements Of Modern Algebra
8th Edition
ISBN:9781285463230
Author:Gilbert, Linda, Jimmie
Publisher:Gilbert, Linda, Jimmie
Chapter2: The Integers
Section2.2: Mathematical Induction
Problem 46E: Use generalized induction and Exercise 43 to prove that n22n for all integers n5. (In connection...
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2)
Using induction on n, prove for all positive integers n that:
2 11"
L1 1.
[F2n + 1
F2n
F2n
F2n – 1
%3D
where F, denotes the nth Fibonacci number.
Transcribed Image Text:2) Using induction on n, prove for all positive integers n that: 2 11" L1 1. [F2n + 1 F2n F2n F2n – 1 %3D where F, denotes the nth Fibonacci number.
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