Asymptotic Analysis and Convergence of Recursively Defined Sequences

The asymptotic properties and limiting behavior of several distinct real sequences are determined. These sequences are defined by means of recurrence relations. Divergent and convergent sequences are discussed. It is shown methods can be found to treat both kinds producing definite knowledge with regard to the sequence. In the case of divergence, a related convergent subsequence can often be found by examining the asymptotic results. Although the methods may have only a limited applicability, some theorems are given to give more of a synthesis to the work.