An Example of the Training a Methodological Competences in Mathematical Analysis

In this paper we try to present some simple methods of training and development of professional competences, more specifically methodological, for obtaining the identities mathematical (combinatorial) and their use. Thus, starting from a simple integral, we obtain multiple identities mathematical (combinatorial), that, then we will use in calculating limits of sequences and some primitives, respectively definite integrals. The attentive reader and interested in these issues will notice that the results of this work complete and definitive resolves many problems of Mathematics. Therefore we consider that the work will be of real help to students who are preparing for competitions and Olympiads, students in deepening their knowledge and passing exams and teachers in their professional training. Of course not here we present all types of exercises that can solve with the formulas proven in the paper. There are other types of exercises than those presented herein and we will present in a forthcoming paper.