Series
Series is the sum of the elements of the Sequence. For example is a sequence with four elements and the corresponding series will be where the sum of the series or value of the series will be 20.
Understanding the Meaning of a Series
A series in mathematics builds on the concept of sequences. If we have a sequence the expression is known as the series associated with that sequence. A series can be finite or infinite, depending on whether the sequence is finite or infinite. Series are often represented in a compact form using sigma notation (Σ), which signifies the summation involved.
So, the series can be abbreviated as
Difference Between Sequence and Series
Sequence | Series |
---|---|
In sequence, elements are placed in a particular
order following a particular set of rules. |
In series, the order of the elements is not
necessary. |
It is just a collection (set) of elements that
follow a pattern. |
It is a sum of elements that
follow a pattern. |
The order of appearance of the numbers is
important. |
The order of appearance of the numbers is
not important. |
Example: Arithmetic Sequence
|
Example: Arithmetic Series
|
Types of Series
Arithmetic Series
An Arithmetic Series is a series formed by using an arithmetic sequence. for example is an arithmetic series.
The arithmetic series is represented by
Geometric Series
A Geometric Series is a series formed by using an geometric sequence. for example is a geometric series.
The geometric series is represented by