Alternating Series Test (Leibniz's Theorem) for Convergence of an Infinite Series

The Alternating Series Test, commonly known as Leibniz's Theorem, stands as a fundamental criterion in the realm of infinite series convergence analysis. At the core of this test lies a distinctive characteristic: the alternating signs of its terms. Developed by the renowned mathematician Gottfried Wilhelm Leibniz, this theorem provides a concise and powerful method to ascertain the convergence of infinite series exhibiting an alternating pattern. By focusing on the interplay of alternating terms, the Alternating Series Test offers a precise criterion for determining whether such series converge, contributing significantly to the understanding of mathematical series and their convergence behavior.