Difference between revisions of "Series"
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==Types of Series== | ==Types of Series== | ||
===Arithmetic Series=== | ===Arithmetic Series=== | ||
An [[ | An [[Sequences#Arithmetic Sequence|Arithmetic Series]] is a series formed by using an arithmetic sequence. for example <math>1+3+5+7+9+11+13+15</math> is an arithmetic series. | ||
===Geometric Series=== | ===Geometric Series=== |
Revision as of 19:21, 31 October 2023
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.
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. |
Order of appearance of the numbers is
important. |
The order of appearance 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.
Geometric Series
A geometric Series is a sequence where every term bears a constant ratio to its preceding term. This ratio is called the "common ratio". The terms of the geometric sequence are of the form
Example: Here
Fibonacci Series
Fibonacci Series is a sequence where every term is the sum of the last two preceding terms.
Example: