(untitled) (European Journal of Pedagogical Initiatives and Educational Practices, 2025)
This paper presents an analysis of the convergence behavior of infinite series within the scope of mathematical analysis. Through the examination of four distinct examples, the study illustrates the application of various convergence tests, including the comparison test, ratio test, alternating series test, and absolute convergence criteria. The aim is to deepen the understanding of when and why a series converges absolutely, conditionally, or diverges. This work serves as both a practical guide and a conceptual reinforcement of series convergence for students and educators in higher mathematics.