The Fibonacci numbers 1, 1, 2, 3, 5, 8, 13.. are defined by the recursion formula xn+1 = Xn + xn-1, whit x1 = 1.Prove that (xn, xn+1) = 1 and that xn (a" – b") /(a – b), where a and bare the roots of the quadratic equation x? – x – 1 = 0. X2 - -
The Fibonacci numbers 1, 1, 2, 3, 5, 8, 13.. are defined by the recursion formula xn+1 = Xn + xn-1, whit x1 = 1.Prove that (xn, xn+1) = 1 and that xn (a" – b") /(a – b), where a and bare the roots of the quadratic equation x? – x – 1 = 0. X2 - -
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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Question
![The Fibonacci numbers 1, 1, 2, 3, 5, 8, 13... are defined by
the recursion formula xn+1 = Xn + Xn-1,
whit
X1 =
1.Prove that (xn, Xn+1) = 1 and that xn
(a" – b") /(a – b), where a and bare the roots of the
quadratic equation x2 – x – 1 = 0.
X2
-
-
-](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fbae59a5a-2099-4735-8f42-c71e71bbba7c%2F2ccda194-d419-4900-87b9-3725c9f5dcab%2Fpup4gmb_processed.jpeg&w=3840&q=75)
Transcribed Image Text:The Fibonacci numbers 1, 1, 2, 3, 5, 8, 13... are defined by
the recursion formula xn+1 = Xn + Xn-1,
whit
X1 =
1.Prove that (xn, Xn+1) = 1 and that xn
(a" – b") /(a – b), where a and bare the roots of the
quadratic equation x2 – x – 1 = 0.
X2
-
-
-
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