<abstract xmlns="http://www.w3.org/1999/xhtml"><p>In this note, we establish some general results for two fundamental recursive sequences that are the basis of many well-known recursive sequences, as the Fibonacci sequence, Lucas sequence, Pell sequence, Pell-Lucas sequence, etc. We establish some general limit formulas, where the product of the first <italic>n</italic> terms of these sequences appears. Furthermore, we prove some general limits that connect these sequences to the number <italic>e</italic>(≈ 2:71828:::).</p></abstract>

In this note, we establish some general results for two fundamental recursive sequences that are the basis of many well-known recursive sequences, as the Fibonacci sequence, Lucas sequence, Pell sequence, Pell-Lucas sequence, etc. We establish some general limit formulas, where the product of the first n terms of these sequences appears. Furthermore, we prove some general limits that connect these sequences to the number e(≈ 2:71828:::).

A Note on Two Fundamental Recursive Sequences

Annales Mathematicae Silesianae

This work is licensed under the Creative Commons Attribution 4.0 International License.

{"article-title":"A Note on Two Fundamental Recursive Sequences"}

In this note, we establish some general results for two fundamental recursive sequences that are the basis of many well-known recursive sequences, as the...

A Note on Two Fundamental Recursive Sequences

Published Online: Jul 27, 2021

Page range: 172 - 183

Received: Jan 08, 2021

Accepted: Jul 07, 2021

DOI: https://doi.org/10.2478/amsil-2021-0007

Keywords
recursive sequence, Binet style formula, the number

© 2021 Reza Farhadian et al., published by Sciendo

This work is licensed under the Creative Commons Attribution 4.0 International License.

A Note on Two Fundamental Recursive Sequences

Published Online: Jul 27, 2021

Page range: 172 - 183

Received: Jan 08, 2021

Accepted: Jul 07, 2021

DOI: https://doi.org/10.2478/amsil-2021-0007

Keywordsrecursive sequence, Binet style formula, the number

© 2021 Reza Farhadian et al., published by Sciendo

This work is licensed under the Creative Commons Attribution 4.0 International License.

Keywords
recursive sequence, Binet style formula, the number