Limits of recurrent sequences

In the present work we study limits of recursively entered sequence an+1 = f(an). We use two approaches. The first doesn't require deeper knowledge than the very concept of limits of sequences. In the second we examine first the situation in general, we focus on the function f and the derived sentences then show how the properties of this function affect the value of the limit of the sequence {an}. This approach goes beyond the normal range of fabrics offered at the bachelor's degree. Reader should significantly expand knowledge regarding the investigation of a particular type of limit sequences. Both approaches are demonstrated not only in theory but also in five specific examples.