Proofs for the Limit of Ratios of Consecutive Terms in Fibonacci Sequence

Chao-Ping Chen; Ai-Qi Liu; Feng Qi

Proofs for the Limit of Ratios of Consecutive Terms in Fibonacci Sequence

Authors

Chao-Ping Chen Department of Applied Mathematics and Informatics, Jiaozuo Institute of Technology, Jiaozuo city, Henan 454000, China
Ai-Qi Liu Sanmenria College of Vocational Technology, Sanmenria City, Henan 472000, China.
Feng Qi Department of Applied Mathematics and Informatics, Jiaozuo Institute of Technology, Jiaozuo city, Henan 454000, China

Keywords:

Ratio, Fibonacci number, limit, golden ratio, Weierstrass-Bolzano theorem, series method, definition of limit, difference equation method, matrix method, algebraic method

Abstract

In the short note, six proofs for the limit of ratios of consecutive terms in Fibonacci sequence are provided, including using Weierstrass-Bolzano theorem, series method, by definition of limit, difference equation method, matrix method, algebraic method.

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Published

2003-10-01

How to Cite

[1]

C.-P. Chen, A.-Q. Liu, and F. Qi, “Proofs for the Limit of Ratios of Consecutive Terms in Fibonacci Sequence”, CUBO, vol. 5, no. 3, pp. 23–30, Oct. 2003.