Sigma Notation (DP IB Analysis & Approaches (AA): HL): Revision Note

Sigma notation

What is sigma notation?

• Sigma notation shows the sum of a certain number of terms in a sequence

• The symbol Σ is the capital Greek letter 'sigma' and stands for 'sum'

• e.g. for $\sum _{r=1}^4{r}^2$

  • The formula after the Σ tells you how to work out each term

    • It is the n^th term formula but written in $r$ instead

  • The lower limit tells you which term to start on

  • The upper limit tells you which term to end on

  • So $\sum _{r=1}^4{r}^2=1^2+2^2+3^2+4^2=30$

• The letter $k$ can also be used (instead of $r$)

• Be careful, as not all lower limits start at 1

  • For example $\sum _{k=0}^4{k}^3$  or  $\sum _{k=7}^{14}(2k-13)$