Continued Fractions and their Interpretations

Author

Christopher Hanusa, Harvey Mudd College

Graduation Year

2001

Document Type

Open Access Senior Thesis

Degree Name

Bachelor of Science

Department

Mathematics

Reader 1

Francis Su

Reader 2

Arthur Benjamin

Abstract

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.

Recommended Citation

Hanusa, Christopher, "Continued Fractions and their Interpretations" (2001). HMC Senior Theses. 127.
https://scholarship.claremont.edu/hmc_theses/127