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IBMathsDPAnalysis & Approaches (AA)SLRevision Notes1. Number & AlgebraSequences & SeriesSigma Notation

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

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Sigma Notation

What is sigma notation?

  • Sigma notation is used to show the sum of a certain number of terms in a sequence

  • The symbol Σ is the capital Greek letter sigma

  • 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

4-5-2-sigma-not-illustr-1

  • Be careful, the limits don’t have to start with 1

    • For example sum from k space equals space 0 to 4 of left parenthesis 2 k plus 1 right parenthesis  or  sum from k space equals space 7 to 14 of left parenthesis 2 k minus 13 right parenthesis

    • r and k are commonly used variables within sigma notation

Examiner Tips and Tricks

  • Your GDC will be able to use sigma notation, familiarise yourself with it and practice using it to check your work

Worked Example

A sequence can be defined by  u subscript n equals space 2 space cross times space 3 to the power of n minus 1 end exponent for  n element of space straight integer numbers to the power of plus . 

a) Write an expression for u subscript 1 space plus space u subscript 2 space plus space u subscript 3 space plus space... space plus space u subscript 6 using sigma notation.

ai-sl-1-2-1-sigma-a

 

b) Write an expression for u subscript 7 space plus space u subscript 8 space plus space u subscript 9 space plus space... space plus space u subscript 12using sigma notation.

ai-sl-1-2-1-sigma-b

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    Amber

    Author: Amber

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    Amber gained a first class degree in Mathematics & Meteorology from the University of Reading before training to become a teacher. She is passionate about teaching, having spent 8 years teaching GCSE and A Level Mathematics both in the UK and internationally. Amber loves creating bright and informative resources to help students reach their potential.