## Journal of Applied Mathematics

- J. Appl. Math.
- Volume 2016 (2016), Article ID 4971594, 6 pages.

### A Method to Construct Generalized Fibonacci Sequences

Adalberto García-Máynez and Adolfo Pimienta Acosta

#### Abstract

The main purpose of this paper is to study the convergence properties of Generalized Fibonacci Sequences and the series of partial sums associated with them. When the proper values of an $s\times s$ real matrix $A$ are real and different, we give a necessary and sufficient condition for the convergence of the matrix sequence $A,{A}^{\mathrm{2}},{A}^{\mathrm{3}},\dots $ to a matrix $B$.

#### Article information

**Source**

J. Appl. Math. Volume 2016 (2016), Article ID 4971594, 6 pages.

**Dates**

Received: 17 September 2015

Accepted: 6 January 2016

First available in Project Euclid: 13 April 2016

**Permanent link to this document**

https://projecteuclid.org/euclid.jam/1460554504

**Digital Object Identifier**

doi:10.1155/2016/4971594

**Mathematical Reviews number (MathSciNet)**

MR3465044

#### Citation

García-Máynez, Adalberto; Acosta, Adolfo Pimienta. A Method to Construct Generalized Fibonacci Sequences. J. Appl. Math. 2016 (2016), Article ID 4971594, 6 pages. doi:10.1155/2016/4971594. https://projecteuclid.org/euclid.jam/1460554504