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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

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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 from r equals 0 to 4 of left parenthesis 2 r plus 1 right parenthesis or sum from r equals 7 to 11 of left parenthesis 2 r minus 13 right parenthesis 

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 plus B r
    • Geometric will have the form A cross times B to the power of 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 from r equals 1 to 6 of left parenthesis 4 r plus 7 right parenthesis plus sum from r equals 7 to 11 of left parenthesis 4 r plus 7 right parenthesis equals sum from r equals 1 to 11 of left parenthesis 4 r plus 7 right parenthesis

sum from r equals 1 to 100 of left parenthesis 7 cross times 2 to the power of r right parenthesis minus sum from r equals 1 to 50 of left parenthesis 7 cross times 2 to the power of r right parenthesis equals sum from r equals 51 to 100 of left parenthesis 7 cross times 2 to the power of r right parenthesis

 

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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    Roger

    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.