MACHINE LEARNING PROBLEM TO STUDY THE CONVERGENCE OF A SERIES BASING ON SUB-SERIES OF THE HAMONIC SERIES

Abstract

In this article, we construct a machine learning approach to implement the procedure of evaluating the convergency of a series in refering to a sub-series of the hamonic series. This approach based on the theory of machine learning creates an automation procedure for the related problem. The results obtained in this article with the clear proofs are helpful. They are developed from the main results about the criteria of convergence for a subseries of the hamonic series which was first proposed by V.T. Dinh et al. This development is directed in the way that the application for such critera become more practical and easier to implement. Therefore, the implementation constructed in the article with the reference to these results is feasible and more efficient. The application could be extended to study the behavior of the approximate solution to ordinary differential equations or partial differential equations with the machine learning approach, as well as the combination of some inovation numerical approaches, such as the Monte-Carlos method.