a) what distinguishes convergent sequences from divergent sequences
When n is approaching to infinity, the convergent sequence is close to a real number not approaching to infinity. For example, the sequence {1/n}, in this sequence, when n is approaching to infinity, 1/n is approaching to 0.
When n is approaching to infinity, the divergent sequences do not approaching to any real number or approaching to infinity. For example 1) {(-1)^n}, in this sequence, we cannot figure out what is the data when n is approaching to the infinity, it can be 1 or -1. 2) {n^2}, in this sequence, when n is approaching to the infinity, the sequence is approaching to the infinity as well.

b) what distinguishes convergent series from divergent series.
Convergent series is the sum of sequences is close to a number. From the ratio rule, when the |r|1 in a series, this series is divergent. For example, the sum of sequence {2^n}.