Strategies to Test an Infinite Series for Convergence

Testing the convergence of an infinite series is a fundamental concept in calculus and mathematical analysis. Various strategies have been developed to determine whether an infinite series converges or diverges, each with its own set of conditions and techniques. These strategies play a crucial role in assessing the behavior and properties of infinite series, aiding in the analysis of functions, sequences, and mathematical models. In this essay, we will explore and elucidate the key strategies employed to test the convergence of infinite series, providing insights into their theoretical foundations and practical applications in mathematical analysis.