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
• 97i30
• 11k31
• 40a05
• 11b39