About this document
Deriving Binet by verosax is a document available to read on EtoBox.
This document summarizes the derivation of the closed formula for Fibonacci numbers. It begins by introducing Fibonacci numbers and their recursive definition. It then presents a general proposition that any sequence defined recursively by xn = bxn-1 + cxn-2 can be written explicitly using the roots of its auxiliary polynomial. Applying this to the Fibonacci sequence leads to its closed formula as Fn = (φn - φ-n)/√5, where φ is the golden ratio. The document concludes by noting analogies between difference
- Author
- verosax
- Language
- EN