Sigma Notation (Edexcel International AS Maths: Pure 2): Revision Note

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

• Be careful – the limits don't have to start with 1!

  • For example: $\sum _{r=0}^4(2r+1)$ or $\sum _{r=7}^{11}(2r-13)$ 

How do I use sigma notation?

• Sigma notation can be used to represent both arithmetic series and geometric series

  • Arithmetic will have the form $A+Br$

  • Geometric will have the form $A\times B^r$

  • Writing out the first few terms will help you

• To work out such a sum use the arithmetic and geometric series formulae

• As long as the expressions being summed are the same you can add and subtract in sigma notation

  • For example:

$\sum _{r=1}^6(4r+7)+\sum _{r=7}^{11}(4r+7)=\sum _{r=1}^{11}(4r+7)$

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