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The harmonic, alternated harmonic and –series with (Basel problem) series,
are some of the most famous infinite series in mathematics and, they are used as examples and counterexamples to illustrate the theory of convergence of series. In this article some of the contributions of the mathematicians who dedicated themselves to the study of the convergence of these three series are presented. The contributions of Nicole Oresme, Pietro Mengoli, Nikolaus Mercator and Leonhard Euler are highlighted.