- (a). Convergent sequences have a finite limit. When n closes to infinity, An close to a finite number. eg. An=1/n. when n is close to infinity, limAn gets closer to 0.
(b). Divergent sequences do not have a finite limit. It means when n is close to infinity, An close to +infinity or -infinity, and it does not close to a finite number. eg. limAn=n. when n is close to infinity, An also gets closer to infinity.
2. (a). Convergent Series: When I add more and more terms of a convergent series, the sum of the series get closer to a certain number. It means the sum of the series have a finite limit. eg. {(2/3)^n} is a convergent series.
(b). Divergent Series: When I add more and more terms of a divergent series, the sum of the series cannot get closer to a certain number. Even if each partial sum gets closer to a certain number, the sum of the whole series get closer to +infinity or-infinity. eg. {1/n}is a divergent series, although limAn=1/n is a convergent sequence.