Grouping of Terms of a Series

Abstract

From a given series we can make a new series by inserting brackets (parentheses) among the terms of the given series that is, making the groups of terms of the series. The terms of the new series are formed by summing the terms of the series within the inserted brackets. If Sy_n is a series obtained from a series Sx­_n by inserting parentheses'(…..)' then Sx_n is also called a series obtained from the series Sy_n by removing parentheses.

Keywords: Grouping, brackets, parentheses, summing, inserting, removing, converges/convergent, diverges/divergent