Two methods of calculating the sum of an infinite sequence of number series

Abstract

The paper presents two methods of calculating the selected infinite sequences of number series. The historical notes used are one of the forms of the motivation of math-ematical activity, since it is believed that the mathematical-pedagogical process should be motivated also in this way. The famous Cicero is, among other things, also famed by saying “Historia est Magistra Vitae”. The paper looks back to the 14th century by focus-ing on Nicolas Oresme who managed to calculate the sums of infinite sequences, alt-hough his approach was a limited one. The other method of calculation rests in the appli-cation of the apparatus of a higher mathematical level which was originated in the 17th century. However, the given sums were calculated only 2 centuries later, when mathe-matics managed to overcome the crisis which it suffered in the 18th century.