ASMaths: Pure 1CIERevision Notes4. Sequences & Series4.4 Further Sequences & Series4.4.2 Sigma Notation

Sigma Notation (CIE AS Maths: Pure 1)

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Roger

Last updated

16 September 2023

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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})

Examiner 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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Author: Roger

Expertise: Maths

Roger's teaching experience stretches all the way back to 1992, and in that time he has taught students at all levels between Year 7 and university undergraduate. Having conducted and published postgraduate research into the mathematical theory behind quantum computing, he is more than confident in dealing with mathematics at any level the exam boards might throw at you.