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Continued Fractions and their Interpretations

The Fibonacci Numbers are one of the most intriguing sequences in mathematics. I present generalizations of this well known sequence. Using combinatorial proofs, I derive closed form expressions for these generalizations. Then using Markov Chains, I derive a second closed form expression for these numbers which is a generalization of Binet’s formula for Fibonacci Numbers. I expand further and determine the generalization of Binet’s formula for any kth order linear recurrence.

Identiferoai:union.ndltd.org:CLAREMONT/oai:scholarship.claremont.edu:hmc_theses-1130
Date01 April 2001
CreatorsHanusa, Christopher
PublisherScholarship @ Claremont
Source SetsClaremont Colleges
Detected LanguageEnglish
Typetext
Formatapplication/pdf
SourceHMC Senior Theses

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