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Abstract(s)
O presente trabalho destina-se a servir de base a um curso de enriquecimento curricular,
na área da matemática, para alunos do secundário. O tema escolhido é séries numéricas.
Apresentamos os conteúdos necessários para definir uma série, os conceitos pertinentes,
assim como muitos resultados que permitem aferir a natureza de uma dada série. Apresentamos
critérios usuais, como são os critérios de condensação de Cauchy, de comparação, da
raiz, da razão, de Kummer, de Gauss, de Leibniz, vimos também resultados menos usuais,
como o critério de Schlomilch, ou os resultados de Moser e Salat. Para estes últimos é
necessário introduzir novos conceitos de convergência, assim como o conceito de densidade
natural.
The present work is intended to serve as a basis for a curricular enrichment course in the area of mathematics for secondary students. The chosen theme is the numerical series. We present the contents necessary to define a series, the pertinent concepts, as well as many results that allow us to gauge the nature of a given series. We present usual tests such as the Cauchy's condensation test, comparison, root, D'Alembert, Kummer, Gauss, Leibniz test, as well as less usual results, such as the Schlomilch test, or the results of Moser and Salat. For the latter it is necessary to introduce new concepts of convergence, as well as the concept of natural density.
The present work is intended to serve as a basis for a curricular enrichment course in the area of mathematics for secondary students. The chosen theme is the numerical series. We present the contents necessary to define a series, the pertinent concepts, as well as many results that allow us to gauge the nature of a given series. We present usual tests such as the Cauchy's condensation test, comparison, root, D'Alembert, Kummer, Gauss, Leibniz test, as well as less usual results, such as the Schlomilch test, or the results of Moser and Salat. For the latter it is necessary to introduce new concepts of convergence, as well as the concept of natural density.
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Keywords
Densidade Natural Série Série Harmónica Subséries Sucessão