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...).

General Limit Formulae Involving Prime Numbers

“…There are also some limit formulae involving recursive sequences that tend to the number e. For example, let F n be the nth Fibonacci number. Following [3] and [5], we have…”