Series convergence refers to the behavior of an infinite series, which is the sum of an infinite sequence of numbers. A series converges if the sum approaches a specific finite value as more terms are added. For example, the series formed by adding fractions like 1/2, 1/4, 1/8, and so on converges to 1. To determine if a series converges, mathematicians often use tests such as the Ratio Test or the Root Test. These methods help analyze the terms of the series to see if they decrease sufficiently fast to yield a finite sum. If a series does not converge, it is said to diverge.