Generalizações de sequências matemáticas no ensino médio: um estudo teórico-prático das recorrências lineares e do princípio de indução matemática

Abstract

This work deals with the Recurrences of 1st order, as useful tools, and feasible to be applied in Basic Education, from the 1st year of High School. The theory will contemplate some algebraic concepts, since these have the capacity to provide the student with the practice and the increase of its potential of generalization and abstraction, as well as to compose an e ective tool in solving mathematical problems. This approach is justi ed because most students, when starting high school, have a very limited knowledge regarding algebra, since many can not really understand the meaning of the variables, that is, it has great dislike for "ready-made formulas ", pre-established by textbooks. The de nitions of concepts and procedures would allow the construction of strategies, formulation of conjectures, as well as the development of attitudinal contents on the part of the student, allowing for the same, through, for example, the Telescopic Sums the construction and apprehension of generalizations, closed formulas and through mathematical demonstrations promoted by the Principle of Mathematical Induction, we would obtain their con rmation or not. Such context is essential for a meaningful and autonomous learning, fundamental for the resolution of diverse situations - problems, be they elementary or Olympic.