Sum and Product Notation

The sum notation uses the capital Greek letter sigma as follows:

Sigma notation

Thus if x1 = 6, x2 = 7 and x3 = -2, then


Note that index i can be replaced by any other index and the results will be the same. Thus,


Also the initial value doesn’t have to be 1. For example, assuming k ≤ n


The initial value can also be –\infty and/or the final value can be +\infty.


We can iterate the use of the sigma notation. For example,



We can also use abbreviated notations such as the following:


There is a similar notation for products using the capital Greek letter pi:

Pi product notation

2 Responses to Sum and Product Notation

  1. Grace says:

    Is it possible to do the Capital Pi (Product) function on Excel?

    Here is what I need to do, using an example with the first three rows (it will go up to 101 rows):

    1st row Y_1=x_1 (1-z_1)
    2nd row Y_2=x_2 (1-z_1)(1-z_2)
    3rd row Y_3=x_3 (1-z_1)(1-z_2)(1-z_3)

    Any advice would be greatly appreciated. Thank you!

    • Charles says:

      There is a product function in Excel that you could use. If R1 is a range then =PRODUCT(R1) returns the value which is the product of the values of all the cells in R1.

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