1. 11.4 Series & Sigma Notation

2. Note: a sequence or series does not have to be arithmetic or geometric
Series = the terms of a sequence added together
Arithmetic sequence:
Note: a sequence or series does not have to be arithmetic or geometric
1, 3, 5, 7, 9, 11
Arithmetic series:
Geometric sequence:
could be neither!!
5, 15, 45, 135
Geometric series:

3. Sigma Notation New notation: ∑  sigma = the sum of
general term?
tn = 1 + (n – 1)(2)
tn = 1 + 2n – 2
= 2n – 1
general term
upper limit  =
lower limit 

4. Example 1 Evens: 2 + 4 + 6 + 8 + … + 100 general term?
tn = 2 + (n – 1)(2)
tn = 2 + 2n – 2
= 2n
Find upper limit:
(what term # is 100)
n is term #
tn = 2n
100 = 2n
50 = n
= 2(1) + 2(2) + 2(3) + 2(4) + …+ 2(50)

5. Ex 2) Write the series in expanded form
any letter 
= (-1)1(1+2)
+ (-1)2(2+2)
+ (-1)3(3+2)
+ …
+ (-1)20(20+2)
= (-1)(3)
+ (1)(4)
+ (-1)(5)
+ …
+ (1)(22)
= – – 5 + … + 22

6. Ex 3) Use sigma notation to write the series
… + 100
Arithmetic
d = 5
t1 = 10
general term?
tn = 10 + (n – 1)(5)
tn = n – 5
= 5n + 5
Find upper limit:
(what term # is 100)
tn = 5n + 5
100 = 5n + 5
 19 = n or
don’t forget parentheses!!

7. Ex 3) Use sigma notation to write the series
series doesn’t end!
(infinite)
Patterns!
Neither arithmetic nor geometric!!
numer: 5
denom: evens
(2n)
alt. signs: (-1)n+1
(since 1st term is positive)
infinity since series doesn’t end
If 1st term is negative, use (-1)n
Check it!!!

8. Homework
#1105 Pg – 23 odd