Difference between revisions of "Series"

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==Types of Series==
==Types of Series==
===Arithmetic Series===
===Arithmetic Series===
An [[Sequences#Arithmetic Sequence|Arithmetic Series]] is a series formed by using an [[Sequences#Arithmetic Sequence|arithmetic sequence]]. for example <math>1+3+5+7+9+11+13+15</math> is an arithmetic series.
An Arithmetic Series is a series formed by using an [[Sequences#Arithmetic Sequence|arithmetic sequence]]. for example <math>1+3+5+7+9+11+13+15</math> is an arithmetic series.


The arithmetic series is represented by a + (a+d) + (a+2d) + (a+3d) + …a<math>a+(a+d)+(a+2d).......</math>
The arithmetic series is represented by a + (a+d) + (a+2d) + (a+3d) + …a<math>a+(a+d)+(a+2d).......</math>

Revision as of 13:05, 1 November 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.

The arithmetic series is represented by a + (a+d) + (a+2d) + (a+3d) + …a

Geometric Series

An Geometric Series is a series formed by using an geometric sequence. for example is a geometric series.

The geometric series is represented by