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Using part (i) prove the result, lim Fn+1 n→∞ Fn = 1+√5 2

Using part (i) prove the result, lim Fn+1 n→∞ Fn = 1+√5 2

Advanced Engineering Mathematics
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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(ii) Using part (i) prove the result, lim Fn+1 n→∞ Fn = 1+√5 2
Transcribed Image Text:(ii) Using part (i) prove the result, lim Fn+1 n→∞ Fn = 1+√5 2
The numbers that appear in the sequence below are called Fibonacci number. 1 1, 1, 2, 3, 5, 8, 13, 21, ....The Fibonacci sequence can be determined by the rule F₁ = 1, F₂ = 1 and Fn = Fn-1 + Fn-2. Using this result and a method of induction, prove F2+1 − Fn+1Fn − F2² = (-1)" for any natural number n.
Transcribed Image Text:The numbers that appear in the sequence below are called Fibonacci number. 1 1, 1, 2, 3, 5, 8, 13, 21, ....The Fibonacci sequence can be determined by the rule F₁ = 1, F₂ = 1 and Fn = Fn-1 + Fn-2. Using this result and a method of induction, prove F2+1 − Fn+1Fn − F2² = (-1)" for any natural number n.
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