👉 In mathematics, a convergent series is one that has a finite sum or limit. In other words, it is a sequence of numbers whose terms get closer and closer together as you add them up or look at their behavior. Examples of convergent series include the harmonic series, which sums to 1/1 = 1, and the geometric series, which sums to an infinite number but has a finite sum. The term "convergence" refers to whether the sequence of numbers in a conver