A note on two fundamental recursive sequences
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...).
Keywords
recursive sequence; Binet style formula; the number e
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Department of Statistics, Razi University, Iran Iran, Islamic Republic of
https://orcid.org/0000-0003-4027-9838
División Matemática, Universidad Nacional de Luján, República Argentina Argentina
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