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 n...
| Main Author: | |
|---|---|
| Format: | Others |
| Published: |
Scholarship @ Claremont
2001
|
| Subjects: | |
| Online Access: | https://scholarship.claremont.edu/hmc_theses/127 https://scholarship.claremont.edu/cgi/viewcontent.cgi?article=1130&context=hmc_theses |
| Summary: | 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. |
|---|