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Title:	On a series of Goldbach and Euler; On a Series of Goldbach and Euler
Author:	Bibiloni, Lluís; Viader, Pelegrí; Paradís, Jaume
Other authors:	Universitat Pompeu Fabra. Departament d'Economia i Empresa
Abstract:	Theorem 1 of Euler s paper of 1737 'Variae Observationes Circa Series Infinitas', states the astonishing result that the series of all unit fractions whose denominators are perfect powers of integers minus unity has sum one. Euler attributes the Theorem to Goldbach. The proof is one of those examples of misuse of divergent series to obtain correct results so frequent during the seventeenth and eighteenth centuries. We examine this proof closelyand, with the help of some insight provided by a modern (and completely dierent) proof of the Goldbach-Euler Theorem, we present a rational reconstruction in terms which could be considered rigorous by modern Weierstrassian standards. At the same time, with a few ideas borrowed from nonstandard analysis we see how the same reconstruction can be also be considered rigorous by modern Robinsonian standards. This last approach, though, is completely in tune with Goldbach and Euler s proof. We hope to convince the reader then how, a few simple ideas from nonstandard analysis, vindicate Euler's work.
Subject(s):	-history of mathematics -infinite series -nonstandard analysis -Statistics, Econometrics and Quantitative Methods
Rights:	L'accés als continguts d'aquest document queda condicionat a l'acceptació de les condicions d'ús establertes per la següent llicència Creative Commons http://creativecommons.org/licenses/by-nc-nd/3.0/es/
Document type:	Working Paper
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