Question 4 The well-known Fibonacci Sequence Fo, F1, F2, ... is generated by the relation Fk = F1 + Fk2 for all integers k 22 with Fo = F1 = 1. Fibonacci Sequence: 1, 1, 2, 3, 5, 8, 13, 21, 34, ... Prove that the terms of Fibonacci Sequence can also be obtained by n+1 n+1 Fn V5 for all integers n20.

College Algebra
7th Edition
ISBN:9781305115545
Author:James Stewart, Lothar Redlin, Saleem Watson
Publisher:James Stewart, Lothar Redlin, Saleem Watson
Chapter8: Sequences And Series
Section8.5: Mathematical Induction
Problem 29E
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Question 4
The well-known Fibonacci Sequence Fo, F1, F2, ... is generated
by the relation F = F1 + Fk2 for all integers k22 with
Fo = F1 = 1.
Fibonacci Sequence: 1, 1, 2, 3, 5, 8, 13, 21, 34, ...
Prove that the terms of Fibonaci Sequence can also be obtained
by
n+1
n+1
V5
for all integers n20.
Transcribed Image Text:Question 4 The well-known Fibonacci Sequence Fo, F1, F2, ... is generated by the relation F = F1 + Fk2 for all integers k22 with Fo = F1 = 1. Fibonacci Sequence: 1, 1, 2, 3, 5, 8, 13, 21, 34, ... Prove that the terms of Fibonaci Sequence can also be obtained by n+1 n+1 V5 for all integers n20.
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