Somas, somatórios e termos não inteiros

Abstract

In this work, whose central theme is the concept of Summation, including its represen tation, interpretation and properties, based on the premise that students feels uncomfor table in performing algebraic manipulations and solving problems where is used the Sigma notation for Summation, we initially conduct a survey of “when” and “how” the idea of Summation is inserted in Brazilian High School and in courses of Degree in Mathematics. We present, in a structured and concise form, the basic part of the theories that deal with the different types of Summation: Classic Summation with a finite quantity of terms, Classic Summation with an infinite quantity of terms (Series), and Fractional Summati ons, which is the name given to a sum with a non-integer number of terms. In particular, this text contains the first disclosure in Portuguese of the theory developed to Fractional Sums. We conclude with the suggestion that the math teachers should carry out detailed studies over the concept of Summations in his initial or continuing training, aiming to im prove his own understanding of the concepts, so that he can more appropriately mediate the learning of his students regarding the theme and yours applications.