A Note on Two Fundamental Recursive Sequences

Annales Mathematicae Silesianae

Farhadian Reza¹  Jakimczuk Rafael² 

[1] Department of Statistics, Razi University, Kermanshah, Iran;División Matemática, Universidad Nacional de Luján, Luján, Buenos Aires, RepúblicArgentina;

关键词: recursive sequence;    binet style formula;    the number e;    97i30;    11k31;    40a05;    11b39;   

DOI  :  10.2478/amsil-2021-0007

来源: DOAJ

【 摘 要 】

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:::).

【 授权许可】

Unknown