a) what distinguishes convergent sequence from divergent sequences
When n is approaching to the infinity, the convergent sequence is close to a real number not approaching to the infinity. For example, the sequence {1/n}, in this sequence, when n is approaching to the infinity, 1/n is approaching to 0.
When n is approaching to the infinity, the divergent sequences do not approach to any real number or approach to the 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 the sequence is close to a number. From the ratio rule, when the |r|< 1 in a series, this series is convergent. For example, the series{1/(n^2)} Divergent series is the sum of the sequence is close to the infinity. From the ratio rule, when the |r|> 1 is a series, this series is divergent. For example, the series {2^n}.