REVIEW AND GENERALIZATION OF THE CONCEPTS OF INFINITE SERIES WITH RELATED TERMINOLOGIES FROM T.M. APOSTOL’S BOOK MATHEMATICAL ANALYSIS

Abstract

The objective of this paper is to explore the general concept of infinite series and definition of few terminologies on the basis of the book Mathematical Analysis written by T. M. Apostol in 1974. Generally, the ordered set of numbers followed by any fixed rule is called a sequence and the combination of terms of sequences by using addition or subtraction sign with a fixed rule is called a series. In precise sense, a sequence defined by the function f : N → R and is denoted by {f(x)} or {an}. The values of a1, a2... are called the terms of the sequence {an}