CHAPTER 10
LESSON 4
Date ____________________
Sigma Notation
AW n/a
MP 6.5
Objective:
 To use sigma notation to write and evaluate series.
A series can be written using the Greek capital letter  (sigma). This notation provides
us with a mathematical “shorthand” for writing and working with various kinds of series.
A series written with sigma notation could have the following form.
7
n
2
n 1
This notation means simply that we replace the variable n with the numbers 1 through 7
respectively, and then add the resulting terms.
7
So,
n
n 1
2
 12  22  32  4 2  52  62  7 2  140
Part I: Converting sigma notation to expanded form
Example 1:
5
Write the series
 2 k in expanded form and compute the sum.
k 1
We replace the variable k with the numbers 1 through 5 respectively, and then add the
resulting terms.
Example 2:
(4n  5) in expanded form, and compute the sum.
8
Write the series
n 3
We replace the variable n with the numbers 3 through 8 respectively, and then add the
resulting terms. Note that the bottom “index” does not necessarily have to equal 1.
Note that this is an arithmetic series.
Example 3:
4
Write the series
1
i1
4i in expanded form, and compute the sum.
i 1
As before, we replace the variable i with the numbers 1 through 4 inclusive, and then add
the resulting terms.
Part II: Converting expanded form to sigma notation
Example 4:
Convert the series 5  9 13 17  21 25  29 to sigma notation.
There are two steps in the conversion process.
Step 1
Find a formula for the general term tn .
Step 2
Since there are 7 terms, we place n 1 under the letter sigma, and the index 7 above the
letter sigma. Then we write the expression 4n  1 to the right of the symbol.
Example 5:
Convert the series 3 12  48 192  768  3072 to sigma notation.
Step 1
Find a formula for the general term tn .
Step 2
Since there are 6 terms, we place n 1 under the letter sigma, and the index 6 above the
n1
letter sigma. Then we write the expression 3 4 to the right of the symbol
Example 6:
50
How many terms are there in the series
3
k 2
?
k 1
Example 7:
9
How many terms are there in the series
3
k 2
?
k 4
Example 8:
800
How many terms are there in the series
3
k 2
?
k 4
(This type of question has been a favorite multiple choice item on past provincial exams.)