Question

whats the difference between a divergent and a convergent series?

Answer 1

converge-come toward a point
diverge- move away from a point

For a divergent series, even if with each successive partial sum you think you're getting closer to a certain number, there is a later partial sum that is not equal to that number. A divergent series can go all over the place, off to infinity or negative infinity, and other kinds of behavior.


As you add more and more terms of a convergent series (taking successive partial sums), you get closer to a certain number, called the limit of the series