Introduzindo a ideia de séries numéricas nos ensinos fundamental e médio

Abstract

This work presents some ideas of problems and activities that may be help elementary and high school teachers to exhibit concepts and theories of numerical series, as well as ideas of convergence, divergence and perception of the infinite. Through simple constructions of rectangles, calculations of their areas and periods, we show how we can make calculations without having to get into the formalities of definitions and formulas. We also present the basics of series applied by summation, simple geometric constructions that suggest an convergence idea and, in a very smooth way, showing the divergence of the Harmonic series. In the end we show some activities that may be complement these ideas, activities that are daily contextualizations and others that are used basic concepts of the study of Mathematics, such as Potentiation, Radiciation, Areas and Circumference Perimeters and Pythagorean Theorem. In Elementary Education activities that involve finite grades and show convergence can be applied as a complement and improvement of content studied. In high school, this work can be used to extract introduction examples studies of Sequences and Numerical Series, Arithmetic Progression and Progression Geometric.