(a)

A sequence is an ordered list of numbers which stem from some sequence term .

Consider an example .

Observe that here we are not adding these numbers.

In series, we take this ordered list of numbers and add them and that why purpose of using capital greek letter sigma  .

.

(b)

A convergent series is a series where the sum of all of its terms is finite.

A divergent series is a series where the sum of all its terms are infinite or its partial term does not approach to a finite number as .

(a) 

A sequence is an ordered list of numbers whereas a series is the sum of a list of numbers.

(b)

A convergent series is a series where the sum of all of its terms is finite.

A divergent series is a series where the sum of all its terms are infinite.