The Treatment of Series for the Verification of Riemann Sums

Abstract

The approach to the treatment of series of the form arises from the need for students in the 1st year of the programs in Mathematics, Physics, and Chemistry Education and Research at the Higher Institute of Educational Sciences of Huíla, who have difficulties in developing it in order to ensure the calculation of areas by means of Riemann sums, , and comparing it with the area bounded by the curve  and the  axis, in the interval , The research aims is to develop elements such as series of the form , in order to ensure the treatment of Riemann sums. The research is descriptive, with a qualitative approach, since it focuses on documentary review and the exploration of informal data resulting from interaction between teachers and students. The information confirmed the lack of an approach to this type of series, which makes it difficult to deal with Riemann sums and their evolution into the Exhaustion Method. In this context, a Didactics of Mathematics is required that postulates the principle of logical and sequential systematicity of contents, where the following may be addressed: i) sums of series of the form , ii) the calculation of areas by Riemann sums, and iii) the calculation of areas by the method of exhaustion. Thus, the article initially addresses the sums of the first n termsof series: arithmetic, squares of terms, cubes of terms, and so on.