Soluções não clássicas para problemas da OBMEP

Abstract

Since 2005 the Brazilian Mathematical Olympiad of Public Schools (OBMEP) is present in many schools involving students and teachers by presenting different problems when compared to traditional models of exercises presented in textbooks. There is some special challenge in questions of OBMEP, requiring creativity in its solutions. Collecting cards and answers of the last OBMEP, in five schools in the municipality of Passo Fundo, held on June 5, 2012, we realized that exercises that involve some kind of recursive solution, there were a large numbers of errors. The objective of this work is to present alternative solutions to some problems of the OBMEP, herewith encourage high school teachers to use recurrence as a tool in building models and general solutions to mathematical problems. For this, we present some basic notes about recursive sequences, as well as a study on mathematical recurrence of first and second order, proving some basic theorems and citing some examples for better understanding of the subject. We finish, solving questions that involve recursive reasoning and that are related to OBMEP highlighting the variety of content of basic education that can be used in solving such problems.