(a) what distinguishes convergent sequences from divergent sequences:
Convergent sequences have a finite limit, but divergent sequences do not have a finite limit. We could say that divergent sequences are the car wipers(stuck between a certain range), and convergent sequences are the triangular pyramid({1/n^2}={1,1/4,1/9,…,1/n^2} the number is getting smaller and smaller).
(b) what distinguishes convergent series from divergent series:
The series is converging when the limit of the sequence of partial sums exists, so I would say that the convergent series are the “down-stairs”(as you building the stairs, you have to build the tallest one first and then gradually getting shorter and shorter), and divergent series are the endless waterfall.
