On the Use of Integrals to Evaluate Series of Rational Terms

TL;DR

This paper explores a method using integral transforms to evaluate convergent series, especially those with rational terms, providing new exact results and generalizations beyond standard references.

Contribution

It introduces a novel integral transform approach for evaluating series of rational terms, including new results not found in existing literature.

Findings

Derived exact values for new classes of series

Generalized a known problem from 'The College Mathematics Journal'

Provided a framework for evaluating series using integrals

Abstract

This article is written with the hope to draw attention to a method that uses integral transforms to find exact values for a large class of convergent series (and, in particular, series of rational terms). We apply the method to some series that generalize a problem published in `The College Mathematics Journal'. Some of the results thus obtained have not been founded in standard references.