A convergent series is a sequence of numbers that, when added together, approaches a specific value as more terms are included. This means that the sum of the series gets closer and closer to a finite number, known as the limit, as the number of terms increases. For example, the series formed by adding fractions like 1/2, 1/4, 1/8, and so on converges to 1. In mathematics, determining whether a series converges is essential for understanding its behavior. Various tests, such as the Ratio Test or Integral Test, can be used to analyze convergence. Convergent series are important in fields like calculus and analysis, where they help in approximating functions and solving equations.