Sigma Notation (Edexcel IAL Maths)

Spec point — 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

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

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

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:

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

$\sum_{r=1}^{100} ( 7×2^r )− \sum_{r=1}^{50} ( 7×2^r )= \sum_{r=51}^{100} ( 7×2^r )$

Exam Hint Be careful when more than one letter appears in a sigma notation question.

Worked Example