Rearranjo de séries numéricas: a influência da reordenação na soma

Abstract

From the early stages of Elementary School, we are taught that “the order of the terms doesn’t alter the result of the sum”, which is, indeed, valid in the case of a finite series. However, because mathematics is a precise and rigorous science, the classic saying stated above is generally false, unless it ends with “in a finite series”. Because academic textbooks on infinite series don’t always address the conditionally convergent series in a thorough manner, the present work aims to complement the research in undergraduate mathematics level studies and related fields, focusing on some theorems that deal with convergency in specific rearrangements of the alternating harmonic series. This dissertation also intends to provide support for undergraduate students that have not yet begun their studies, by presenting an introduction on the subject, and adding in a pedagogic sequence intended on facilitating the comprehension and illustrating how some rearrangements work, while questioning the famous statement “the order of the terms doesn’t alter the result of the sum”.