Annales Mathematicae Silesianae (Sep 2021)

A Note on Two Fundamental Recursive Sequences

  • Farhadian Reza,
  • Jakimczuk Rafael

DOI
https://doi.org/10.2478/amsil-2021-0007
Journal volume & issue
Vol. 35, no. 2
pp. 172 – 183

Abstract

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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:::).

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