Direct Comparison Test for Convergence of an Infinite Series

The Direct Comparison Test serves as a fundamental tool in the analysis of the convergence of infinite series within the realm of calculus and mathematical analysis. As an indispensable method, it allows mathematicians to assess the convergence behavior of a given series by comparing it with another known series with well-understood convergence properties. By establishing clear criteria for comparison, this test provides insights into the convergence or divergence of series, enabling mathematicians to discern the behavior of complex mathematical constructs with precision and rigor. In this essay, we delve into the principles, applications, and limitations of the Direct Comparison Test in the context of infinite series convergence analysis.