Sobre una sèrie de Goldbach i Euler Authors Lluís Bibiloni i Matos Pelegrí Viader i Canals Jaume Paradís Abstract Theorem 1 of Eulers paper of 1737 «Variae observationes circa series unfinitas », states the astonishing result that the series of all unit fractions whose denominators are perfect powers of integers minus unity has sum 1. 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 closely and, with the help of some insight provided by a modern (and completely different) 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 Eulers proof. We hope to convince the reader then how a few simple ideas from nonstandard analysis vindicate Eulers work. Downloads Text complet (Català) Published 2008-02-28 How to Cite Bibiloni i Matos, L., Viader i Canals, P., & Paradís, J. (2008). Sobre una sèrie de Goldbach i Euler. Butlletí De La Societat Catalana De Matemàtiques, 22(2), 117–134. Retrieved from https://revistes.iec.cat/index.php/BSCM/article/view/33948.001 More Citation Formats ACM ACS APA ABNT Chicago Harvard IEEE MLA Turabian Vancouver Download Citation Endnote/Zotero/Mendeley (RIS) BibTeX Issue Vol. 22 No. 2 (2007) Section Articles License The intellectual property of articles belongs to the respective authors.On submitting articles for publication to the journal Butlletí de la Societat Catalana de Matemàtiques, authors accept the following terms:Authors assign to Societat Catalana de Matemàtiques (a subsidiary of Institut d’Estudis Catalans) the rights of reproduction, communication to the public and distribution of the articles submitted for publication to Butlletí de la Societat Catalana de Matemàtiques.Authors answer to Societat Catalana de Matemàtiques for the authorship and originality of submitted articles.Authors are responsible for obtaining permission for the reproduction of all graphic material included in articles.Societat Catalana de Matemàtiques declines all liability for the possible infringement of intellectual property rights by authors.The contents published in the journal, unless otherwise stated in the text or in the graphic material, are subject to a Creative Commons Attribution-NonCommercial-NoDerivs (by-nc-nd) 3.0 Spain licence, the complete text of which may be found at https://creativecommons.org/licenses/by-nc-nd/3.0/es/deed.en. Consequently, the general public is authorised to reproduce, distribute and communicate the work, provided that its authorship and the body publishing it are acknowledged, and that no commercial use and no derivative works are made of it.The journal Butlletí de la Societat Catalana de Matemàtiques is not responsible for the ideas and opinions expressed by the authors of the published articles.