## Mentor/s

Hema Gopalakrishnan

## Participation Type

Paper Talk

## Abstract

The Fibonacci sequence is defined as the sequence F_{n} with the recurrence relation F_{n+1} = F_{n} + F_{ n-1} where F_{0 }= 0 and F_{1}= 1. A closely related sequence to the Fibonacci sequence is the Lucas sequence, L_{n}. The terms of the Lucas sequence satisfy the the same recurrence relation as the Fibonacci sequence with differing initial conditions. In this paper, we will study some of the properties of the Fibonacci numbers and explore some of the relationships between Fibonacci and Lucas numbers. We will also give a proof of Binet's explicit formula for computing the n^{th} Fibonacci number.

## College and Major available

Mathematics

## Location

Session 5: Digital Commons & Martire Room 217

## Start Day/Time

4-25-2024 12:30 PM

## End Day/Time

4-25-2024 1:45 PM

## Creative Commons License

This work is licensed under a Creative Commons Attribution-Noncommercial 4.0 License

## Prize Categories

Most Scholarly Impact or Potential, Most Creative, Best Writing

Fibonacci Numbers

Session 5: Digital Commons & Martire Room 217

The Fibonacci sequence is defined as the sequence F_{n} with the recurrence relation F_{n+1} = F_{n} + F_{ n-1} where F_{0 }= 0 and F_{1}= 1. A closely related sequence to the Fibonacci sequence is the Lucas sequence, L_{n}. The terms of the Lucas sequence satisfy the the same recurrence relation as the Fibonacci sequence with differing initial conditions. In this paper, we will study some of the properties of the Fibonacci numbers and explore some of the relationships between Fibonacci and Lucas numbers. We will also give a proof of Binet's explicit formula for computing the n^{th} Fibonacci number.

## Students' Information

Maya Salamone, Mathematics Major, 2024 Graduation