Progressões e somatórios nos vestibulares militares

Abstract

We began this work making a summary in the history of numerical sequences, where we, in chronological order, shown the contributions given by many mathematicians. Continuing our work, we presented a topic of induction, presenting the principle of mathematical induction and its application to solve practical problems, such as the problem of Steiner pizza and Fibonacci rabbits. In the third chapter, we discuss the arithmetic progressions, with some theorems such as the general term, the sum of the fi rst n terms and closed the chapter by some practical applications in simple interest. In Chapter 4 we discuss the geometric progression where we present various properties, formulas for obtaining the general term, the sum of the fi rst n terms, harmonic progressions. In order to present the arithmetic-geometric progressions showing the formula of finite and infi nite sum of its terms, concluding with practical applications of simple and compound interest, arithmetic means, geometric. The chapter 4 begins with infi nite sums, where we present the limit of a sequence, a small approach to harmonic and geometric series, ending with the problem of Von Neumann y and the problem of the bouncing ball. Finally, the work with problems on college entrance exams, especially the vestibular of Instituto Tecnológico de Aeronáutica (ITA), Escola Preparatória de Cadetes do Exército (EsPCEx), Instituto Militar de Engenharia (IME) e da Academia da Forçca Aérea (AFA).