Problemas resolvidos sobre sequências no treinamento de estudantes do ensino médio para Olimpíadas Internacionais de Matemática

Abstract

The International Mathematical Olympiad (IMO) is a competition for high school students in which the number of participants has grown steadily over time. The goals of IMOs are to discover, stimulate and challenge talented students in Mathematics. The Brazilian delegation made its first appearance in 1979 and has improved performance over time. In this dissertation 26 problems that have been proposed for some of the IMO versions and which, in one way or another use sequences in their formulation, are presented and discussed in detail. The intention is that these can be used to train students preparing for international olympics. The material can also be used by university teachers and students. The problems appear organized in four chapters: Algebra, Number Theory, Combinatorics and Geometry. However, typically each problem uses knowledge linked to more than one area of Mathematics. Within each chapter a section is dedicated to each problem and they are ordered by the year in which the IMO took place, from the most recent to the oldest. In several sections we first present an introduction to the key knowledge for solving the problem.