Sigma notation - Sequences and Series

Sigma notation

Don't you find it tiring when we express a series with many terms using numerous addition and/or subtraction signs? Don't you wish that we have something to symbolise this action? Well we have a solution, introducing the "Sigma Notation"! In this section, we will learn how to utilise the sigma notation to represent a series, as well as how to evaluate it.


i=1n\sum_{i=1}^n(an equation containing ii)

\sum : "Sigma"; summation of ithi^{th} term to nthn^{th} term
ii : index, a counter for the ithi^{th} term
nn : index of ending term
  • 1.
    Evaluate the following arithmetic series:
  • 3.
    Evaluate the following geometric series:
  • 6.
    Evaluate the following infinite geometric series:
  • 7.
    Write the following sum in sigma notation, then evaluate
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Sigma notation

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