## Series Sigma Notation (basic)

A series can be described using sigma notation

So what does sigma notation look like? Let’s look at an example

This tells us that we a dealing with series with terms that are of the form

- The first term is when
- The next is when
- We continue in this manner by adding one each time to r until r = 7
- Each of these terms is added.

So we have

### Summing a series given in sigma notation

The least technical method would be to use the one above.

Example

Find S, if

You have noticed that we could have written as a simplification:

And it does follow that

### Arithmetic representations in sigma notation

A sigma expression in the form where ‘a’ and ‘b’ are constants will produce an arithmetic series, with a common difference of ‘a’ and a starting value of ‘a+b’. Using this imformation we could sum a series of this form using the formulae we learnt for arithmetic series.

Examples

Calculate

This is an arithmetic series

Calculate

This is an arithmetic series

The required value is

### Geometric representations in sigma notation

A sigma expression in the form , where the first term is and the common ratio is .

Example

Calculate

This is a geometric series