Question

what is difference between sequence and series

Answer 1

What is difference between sequence and series?

Solution:

A sequence is a list of numbers. The order in which the numbers are listed is important, so for instance

1, 2, 3, 4, 5, ...

is one sequence, and

2, 1, 4, 3, 6, 5, ...

is an entirely different sequence. A series is a sum of numbers. For example,

$$1 + \frac{1}{2} + \frac{1}{4} + \frac{1}{8} + \frac{1}{16} + \dots$$

is an example of a series. A series is composed of a sequence of terms that are added up.

A series, in turn, can be associated with the sequence of its terms;

for instance,

$$1 + \frac{1}{4} + \frac{1}{16} + \frac{1}{64} + \dots$$

can be associated with

$$1, \frac{1}{4}, \frac{1}{16}, \frac{1}{64}, \dots$$

which are simply the terms without the addition signs.

Basic difference between sequence and series is that a sequence is simply a list of numbers, whereas a series is a sum of numbers.