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Wake Use this formula to verit mil of quotient of convecutive numbers is the golden ration: lim n-78 fnti Fn 1+√√5 2 1

Wake Use this formula to verit mil of quotient of convecutive numbers is the golden ration: lim n-78 fnti Fn 1+√√5 2 1

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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1. The Fibonacci sequence is the sequence defined by the following reaussion : F₂=0 F₁ = ¹, F = Food + fn-2 (nzu) Thus the first two terms are o and I and every other from term is obtained by adding together the two previour terms. It turns out that there is an explicit formula that gives the n-th term of the Fibonacci sequence, it is √/= (1+√5)² F = 1 - Jim 4-78 Leter thote Use this formula to verify that the limit of quotient of consecutive Fibonacci numbers is the golden ration: fnt! Fn 1 √5 ~ (₁ = √5)² 2 1+√√5 2
Transcribed Image Text:1. The Fibonacci sequence is the sequence defined by the following reaussion : F₂=0 F₁ = ¹, F = Food + fn-2 (nzu) Thus the first two terms are o and I and every other from term is obtained by adding together the two previour terms. It turns out that there is an explicit formula that gives the n-th term of the Fibonacci sequence, it is √/= (1+√5)² F = 1 - Jim 4-78 Leter thote Use this formula to verify that the limit of quotient of consecutive Fibonacci numbers is the golden ration: fnt! Fn 1 √5 ~ (₁ = √5)² 2 1+√√5 2
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