Writing Sigma Notation

Date: 02/03/99 at 09:29:38
From: Mary Kern
Subject: Writing Sigma Notation

I am tutoring a high school student in Integrated Math 3. She is using 
sigma notations in finite arithmetic and geometric series. I can help 
her with the equations to determine the sum, etc., but I do not 
understand the equation below the sign. Where does it come from?  

Thank you.

Date: 02/03/99 at 18:44:05
From: Doctor Cavallari
Subject: Re: Writing Sigma Notation

I'll try to describe what each part means and give a few examples for 
you.  Here's one to look at for now:

     7
    ----
    \    
    /     2*N
    ----
     N=3  

Sigma notation (also called summation notation) is shorthand for 
summing a series. The expression to the right of the Sigma is the 
formula that you plug each number in the series into.

The equation below the Sigma (N=3 in this example) tells you two 
things. First, it tells you which letter (in the expression to the 
right) you are going to put the values into. Here, that letter is N. 
Second, it tells you what number to start at. So, in this example, we 
are going to start at the number 3 and work our way up.

The number above the Sigma (7) is the number that you go up to (and 
include) when plugging in values. It is not necessarily the number of 
terms in the series.

In the above example, we will input the whole numbers from 3 to 7 
(3,4,5,6,7).

So, our example problem will look like:

     7
    ----
    \    
    /     2*N  =  2*3 + 2*4 + 2*5 + 2*6+ 2*7 = 50
    ----
     N=3


Here is another example for you:

     8
    ----
    \    
    /     I+3  =  5+3 + 6+3 + 7+3 + 8+3 = 38
    ----
     I=5  

See also:

  Summation notation
  http://www.math.uni.edu/~campbell/stat/Sigma.html   

- Doctor Cavallari, The Math Forum
  http://mathforum.org/dr.math/