# Generalized Identities of Certain Continued Fractions

## TL;DR

This paper introduces new generalized identities for continued fractions, linking them to Fibonacci and Lucas numbers, with proofs based on induction, expanding the mathematical understanding of these structures.

## Contribution

It presents novel generalized identities for continued fractions and connects them to Fibonacci and Lucas numbers, using inductive proofs.

## Key findings

- New generalized identities for continued fractions
- Connections established between continued fractions and Fibonacci/Lucas numbers
- Proofs based on induction

## Abstract

In this article, we will discover some new generalized identity regarding continued fractions. We will connect the results to Fibonacci numbers and Lucas numbers. For all the proof, we will use induction.