Name: Sigma Notation (4.4.2) | CIE AS Maths: Pure 1 Revision Notes 2020 Membership
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4.4.2 Sigma Notation

What is sigma notation?

The symbol Σ is the capital Greek letter sigma – that's why it's called 'sigma notation'!
'Σ' stands for 'sum' – the expression to the right of the Σ tells you what is being summed, and the limits above and below tell you which terms you are summing

Sigma Not Illustr 1, A Level & AS Level Pure Maths Revision Notes

Be careful – the limits don't have to start with 1!
- For example: $\sum_{r = 0}^{4} (2 r + 1)$ or $\sum_{r = 7}^{11} (2 r - 13)$

What do I need to be able to do with sigma notation?

Sigma notation can be used to represent both arithmetic progressions and geometric progressions
- Arithmetic will have the form $A + B r$
- Geometric will have the form $A \times B^{r}$
- Writing out the first few terms will help you

Sigma Not Illustr 3, A Level & AS Level Pure Maths Revision Notes

To work out such a sum use the formulae for the sum of arithmetic and geometric progressions
As long as the expressions being summed are the same you can add and subtract in sigma notation
- For example:

\sum_{r = 1}^{6} (4 r + 7) + \sum_{r = 7}^{11} (4 r + 7) = \sum_{r = 1}^{11} (4 r + 7)

\sum_{r = 1}^{100} (7 \times 2^{r}) - \sum_{r = 1}^{50} (7 \times 2^{r}) = \sum_{r = 51}^{100} (7 \times 2^{r})

Exam Tip

Be careful when more than one letter appears in a sigma notation question. Sigma Not Illustr 5, A Level & AS Level Pure Maths Revision Notes

Worked Example

Sigma Not Example, A Level & AS Level Pure Maths Revision Notes

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CIE AS Maths: Pure 1

Revision Notes

4.4.2 Sigma Notation

What is sigma notation?

What do I need to be able to do with sigma notation?

Exam Tip

Worked Example

Author: Roger

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