Analisando séries numéricas: um estudo de convergência e aplicação

Abstract

Abstract This material, organized into six chapters, presents a literature review on convergent numerical series, drawing inspiration from the works of prominent mathematicians mentioned throughout the study. It begins with a concise introduction providing historical context for the topic. The next two chapters outline the properties of sequences and series, as well as applications considered essential for undergraduate mathematics students—knowledge that also has future implications for high school education. Building on the first three chapters, the work moves to its central focus: Raabe's Test. This method offers greater scope than the D’Alembert (Ratio) and Cauchy (Root) tests; although often overlooked in undergraduate curricula, it serves as a valuable tool for specific cases in the study of numerical series. The fifth chapter explores the relationship between convergent numerical series and geometric progressions (GP)—a concept first introduced in high school through the study of finite GP sums. Finally, the conclusion presents a summary of the work, the intended outcomes regarding the proposed criteria and applications, and observations derived from the literature review on the subject. Keywords: Sequences. Numerical Series. Raabe's Test. Geometric Progression.