Coeficientes binomiais estendidos: algumas propriedades e aplicações para o ensino médio

Abstract

The aim of this work is to present a theoretical material about extended binomial numbers, to treat some of their properties and propose the approach of this content in high school. In basic education the definition of binomial numbers, as well the study of their properties, are restricted to nonnegative integers. Using a simple approach, we will start with the study of counting, defining binomial numbers for nonnegative integer values and their properties. We will illustrate the identities in the classic Pascal triangle and then define the binomial coefficients for actual values. At the end of this work, we will propose some activities with resolutions to be applied to high school students.