Algorithms for Calculating the Limits of Convergent Infinite Series

Abstract

We use algorithms to calculate the exact limits of a wide range of convergent infinite series by means of special functions, these are polygamma functions. However, in the case of alternating series, these algorithms do not allow the use of such functions, but allow them to find the limits of this series. Finally, these methods are used as a powerful and simple tool for calculating the limits of many infinite series as shown in the examples included.