Final answer:
A convergent infinite series is a series whose terms approach a finite limit as the number of terms increases, while a divergent infinite series is a series whose terms do not approach a finite limit.
Step-by-step explanation:
In calculus, a convergent infinite series is a series whose terms approach a finite limit as the number of terms increases. This means that the sum of the series exists and is a real number. For example, the infinite series 1/2 + 1/4 + 1/8 + ... is a convergent series because the terms become smaller and eventually approach zero.
On the other hand, a divergent infinite series is a series whose terms do not approach a finite limit as the number of terms increases. This means that the sum of the series does not exist or is infinite. For example, the infinite series 1 + 2 + 3 + ... is a divergent series because the terms increase without bound.