30, November 2025

An Innovative Approach to the Summation and Generalization of Alternating Series

VOLUME-11; ISSUE-11; NOV-2025

Author(s): Dr. Gunjan A. Ranabhatt

Authors Affiliations:

Assistant Professor, Government Engineering College, Bhavnagar, Gujarat Technological University, Ahmedabad, Gujarat,

DOIs:10.2015/IJIRMF/202511029     |     Paper ID: IJIRMF202511029


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 This paper presents a new analytical approach for the evaluation and generalization of certain alternating series involving positive integers. Using an integration-based technique, exact closed-form expressions for the sums of these series are obtained. Several theorems are established to demonstrate the convergence and summation behavior of the considered series. Corresponding corollaries are derived for specific integer values, revealing interesting relationships among even and odd cases. The proposed method extends and unifies earlier results on generalized alternating series, offering a more direct and simplified means of obtaining their exact sums.

Alternating series, Generalization, Exact sum, Convergence, Analytical approach

Dr. Gunjan A. Ranabhatt (2025); An Innovative Approach to the Summation and Generalization of Alternating Series, International Journal for Innovative Research in Multidisciplinary Field, ISSN(O): 2455-0620, Vol-11, Issue-11, Pp. 177-181.          Available on –   https://www.ijirmf.com/

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