Difference between revisions of "Series"

Revision as of 19:25, 31 October 2023

Series is the sum of the elements of the Sequence. For example $2,4,6,8$ is a sequence with four elements and the corresponding series will be $2+4+6+8$ 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 $1,3,5,7,9,11,13,15$	Example: Arithmetic Series $1+3+5+7+9+11+13+15$

Types of Series

Arithmetic Series

An Arithmetic Series is a series formed by using an arithmetic sequence. for example $1+3+5+7+9+11+13+15$ is an arithmetic series.

Geometric Series

An Geometric Series is a series formed by using an geometric sequence. for example $1+2+4+8+16+32$ is an geometric series.

Fibonacci Series

Fibonacci Series is a sequence where every term is the sum of the last two preceding terms.

Example:

$0,1,1,2,3,5,8,13,21,34$

@@ Line 33: / Line 33: @@
 ===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 <math>a,ar,ar^2,......
+An [[Index.php?title=Sequences#Geometric Sequence|Geometric Series]] is a series formed by using an geometric sequence. for example <math>1+2+4+8+16+32</math> is an geometric series.
-</math>
-Example: <math>1,4,16,64,.......</math> Here <math>a=1,d=4</math>
 ===Fibonacci Series===
 Fibonacci Series is a sequence where every term is the sum of the last two preceding terms.