Fibonacci numbers and finite continued fractions

• Main Authors: Go, Aurea Marietta G., Machica, Abegail S.
• Format: text
• Language: English
• Published: Animo Repository 1997
• Subjects: Fibonacci numbers; Continued fractions; Number theory
• Online Access: https://animorepository.dlsu.edu.ph/etd_bachelors/16443
• Institution: De La Salle University

This research paper deals with the study of the Fibonacci Numbers and Continued Fractions. The Fibonacci Sequence is a sequence in which each term is computed by adding the preceding two terms, the first two terms being 1. The terms of this sequence are called Fibonacci Numbers. Some of the identities involving Fibonacci Numbers are included in this paper. The quotient of two successive Fibonacci Numbers can be expressed as the simple finite continued fraction [1 1,1,...1,1] where the integer 1 appears (n + 1) times. Continued Fractions deal with the resolution of fractions into unit fractions. All the theorems, lemmas and corollaries stated in this research paper are part of the discussion in the book entitled Elementary Number Theory by David M. Burton. The researchers expounded on the subject by giving detailed proofs and examples on the theorems, corollaries and lemmas concerning the said topic. Most of the proofs were presented using the Euclidean Algorithm and Mathematical Induction. Some knowledge about Number Theory was also provided in this paper since it is needed for better understanding of some of the proofs.