A convergent series is a mathematical series in which the sum of its terms approaches a finite limit as the number of terms increases.
The convergence of a series is determined by taking the limit of the series as the number of terms approaches infinity. If this limit exists and is finite, then the series is said to converge.
A convergent series has a finite limit as the number of terms approaches infinity, while a divergent series does not have a finite limit and either grows or oscillates indefinitely.
The partial sums of a convergent series approach its limit as the number of terms increases. As a result, the partial sums can be used to estimate the value of the limit.
Convergent series are used in a variety of fields, including physics, engineering, and economics, to model and analyze real-world phenomena. They can also be used to solve equations and make predictions about the behavior of systems.