Sequências de números reais e as famosas constantes matemáticas e, π e ϕ

This work presents a proposal for the study on sequences of real numbers, especially in high school. From the de nition of a sequence, we study the particular cases of arithmetic and geometric progressions. As we know, it is usual for textbooks to terminate the subject of sequences here, but in this...

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Detalles Bibliográficos
Autor: Gregio, Bruno Chioderoli [UNESP]
Tipo de recurso: tesis de maestría
Estado:Versión publicada
Fecha de publicación:2017
País:Brasil
Institución:Universidade Estadual Paulista (UNESP)
Repositorio:Repositório Institucional da UNESP
Idioma:portugués
OAI Identifier:oai:repositorio.unesp.br:11449/150789
Acceso en línea:http://hdl.handle.net/11449/150789
Access Level:acceso abierto
Palabra clave:Sequências de números reais
Limite
Sequências de Cauchy
Sequence of real numbers
Limit
Cauchy sequences
Descripción
Sumario:This work presents a proposal for the study on sequences of real numbers, especially in high school. From the de nition of a sequence, we study the particular cases of arithmetic and geometric progressions. As we know, it is usual for textbooks to terminate the subject of sequences here, but in this work we have advanced the studies presenting the notion of limit of a sequence and the main results on convergent sequences. Having understood that each real number can be obtained as the limit of a Cauchy sequence of rational numbers, we introduce the famous mathematical constants e, π and ϕ, beyond the numbers of the form √a, as the limit of certain Cauchy sequences of rational numbers.