Convergence of series

Convergence of a series refers to the idea of whether the sum of its terms approaches a specific value as more terms are added. Imagine adding smaller and smaller pieces together; if their total gets closer to a certain number, the series converges. If the sum keeps increasing or fluctuating indefinitely, it diverges. For example, if you add fractions like 1/2, 1/4, 1/8, and so on, the total approaches 1. Understanding convergence helps in various fields, including mathematics and finance, to determine stable outcomes from potentially infinite processes.