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7.1a Notes on Sigma Notation Introduction
ending value

(function of k)
k = starting value
What does Sigma Notation look like?
5
 n  1 2  3  4  5
n 1
5
 n3  33  43  53
n
3
 13  23  33  43  53
n 1
4
1
1
1
1
 n  1 2  3  4
n 3
*Note that we have
5
n 1
5
5
n 1
i 1
 n   i . The “n” and the “i" just play the role of dummy variables.
Example 1: Write each of the following in sigma notation
a. 3  6  9  12  ...  60
b. 1 
1 1 1
1
   ... 
4 7 10
3n  1
c. 3 x  6 x 2  9 x 2  12 x 4  ...  60 x 20
d. 1 
x 2 x 4 x6
x2n
   ... 
2! 4! 6!
(2n)!
Example 2: Write out each of the following sums.
6
a.
n
4
n 1
k 1
k
k 3
7
b.

n
c.
 (2i  1)
i 2
n
d.
2
k 1
xk
k 0
(1) k x k

k 0 2 k  1
n
e.
Example 3: Express each of these sums using sigma notation.
a. 1  4  9  16  25  36
b. 3  5  7  9  11 13  15
c.
1 1 1 1 1 1
    
2 5 8 11 14 17
d.
2 3 4
n 1
   ... 
3 4 5
n2
2
3
4
2 n1
e. 2  2  2  2  ...  2
3
5
7
31
f. 2 x  4 x  6 x  ...  30 x
Homework: p. 463:21-34 all. Find/expand sigma notation. Don’t identify pieces or calculate the value.