Chapter 8.2, Problem 1E

a.

To determine

To find: The difference between a sequence and a series.

Answer to Problem 1E

In mathematics, a sequence is defined as an arrangement of numbers in a particular order and a series is defined as the sum of the elements of a sequence.

Explanation of Solution

Given information: A sequence and a series.

Calculation: In mathematics, a sequence is defined as an arrangement of numbers in a particular order and a series is defined as the sum of the elements of a sequence.

Let’s see the difference between a sequence and a series,

Sequence	Series
A sequence is an arrangement of numbers in a particular order.	A series is the sum of the elements of a sequence.
Sequence is a calculable series of items	. A series is any number of items as a set .
A sequence is a list of numbers placed in a defined order while a series is the sum of such a list of numbers.	The series corresponds to a sequence is the sum of the numbers in that sequence

b.

To determine

To find: Convergent series and divergent series.

Answer to Problem 1E

Explanation of Solution

Given information: Convergent series and divergent series

Calculation:

Convergent series- A series is convergent if the sequence of its partial sums tends to a limit, that means the partial sums become closer and closer to a given number when the number of their terms increases.

Divergent series-A divergent series is an infinite series that is not convergent, that means the infinite sequence of the partial sums of the series does not have a finite limit.