The sum of the first n squares of these numbers is a product of two consecutive ones, and the generating function for these numbers is x over the quantity one minus x minus x-squared.
The sum of the first n squares of these numbers is a product of two consecutive ones, and the generating function for these numbers is x over the quantity one minus x minus x-squared. These numbers are given by Binet's formula. This sequence satisfies the same pattern as the Lucas Sequence, and the ratio of successive terms in this sequence approaches (*) phi, the golden ratio. Many of these numbers appear in nature and this sequence was originally used by Leonardo of Pisa to model the reproduction of bunnies. For ten points, identify this sequence beginning one, one, two, three, five, in which each term is the sum of the prior two.
The sum of the first n squares of these numbers is a product of two consecutive ones, and the generating function for these numbers is x over the quantity one minus x minus x-squared.
{Fibonacci} sequence