# Econometric Theory/Summation and Product Operators

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To sum a series of variables , the Greek capital letter sigma *Σ* is used:

.

There are some properties concerning the summation operator *Σ*:

1. , where k is a constant.

2. , where k is a constant.

3. , where *a* and *b* are constants. This is a result of rules 1 and 2 above.

4. ,

The double summation operator is used to sum up twice for the same variable:

The double summation operator has the following properties:

1. . The order of the summation signs is interchangeable.

2. .

3. .

4. .

Finally, the product operator *Π* is defined as: .

## Bibliography[edit]

- Gujarati, D.N. (2003).
*Basic Econometrics, International Edition - 4th ed.*. McGraw-Hill Higher Education. pp. 869-870. ISBN 0-07-112342-3.