Sigma Notation

    In order to understand Riemann sums and integration theory correctly it is important to understand summations using sigma notation.

Definition (Sigma Notation) If are real numbers such that then the summation of these numbers written in sigma notation is



and also using functional notation,



where The is called the index of summation, the is called the th term of the sum, and the upper and lower bounds of the summation are and respectively.

Example (Sigma Notation) Write the sum in expanded form.

    Solution. In expanded form, the sum is

Example (Sigma Notation) Write the sum in expanded form.

    Solution. In expanded form, the sum is

Example (Sigma Notation) Write the sum   in sigma notation.

    Solution. We find that
    

Example (Sigma Notation) Write the sum in sigma notation.

    Solution.  In sigma notation, we have

Example (Sigma Notation) Write the sum



in sigma notation.

    Solution. We find that
    

    

Example (Sigma Notation) Write the sum



in sigma notation.

    Solution. We find that

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Sigma Notation
Published by Library of Math -- Online math organized by subject into topics.
Written by Smith, David A.
http://www.libraryofmath.com/sigma-notation.html