An estimate of the rate of convergence of infinite matrices and their application to infinite series

Author(s): Suresh Kumar Sahani1, A.K. Thakur2, Avinash Kumar3, K. Sharma4
1Department of Science and Technology, Rajarshi Janak University, Janakpurdham, Nepal
2Department of Mathematics, G. G. V., Bilaspur, India
3Department of Mathematics, Dr. C. V. Raman University, India
4Department of Mathematics, NIT, Uttarakhand, Srinagar (Garhwal), India
Copyright © Suresh Kumar Sahani, A.K. Thakur, Avinash Kumar, K. Sharma. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

This study introduces theorems concerning matrix products, which delineate the transformations of sequences or series into other sequences or series, ensuring either the preservation of limits or the guarantee of convergence. Previous literature has explored the properties of matrices facilitating transformations between sequences, series, and their combinations, with detailed insights available in references [1,2,3].

Keywords: Infinite series; matrices; convergence; sequence-to-sequence