11-4 Intro to Series

1
11-4 Intro to Series

• Definition
• A series is the sum of the terms of a sequence.
• Sequence vs. Series
• 2, 4, 8, 2 4 8
  

2
nth Partial Sum

• The nth partial sum is the sum of the first n
  terms of that series.
• Sn sum of the first n terms

3
Sigma Notation
New notation ?
? sigma the sum of
tn FORMULA
upper limit ?
1 3 5 7 9 11 36
lower limit ?
4
TOO

• Evaluate the expression

3(1) 3(2) 3(3) 3(4) 3 6
9 12 30
5
Ex 2) Evaluate the expression
(-1)1(12)
(-1)2(22)
(-1)3(32)
(-1)(3)
(1)(4)
(-1)(5)
3 4 5 -4
6
Sigma Notation

• We want
• Where tk is the formula to find the value of the
• nth term.
• Arithmetic tk t1 (n-1)d
• Geometric tk t1(r)n-1

7
How to Write Sigma Notation

• Write Sn using sigma notation
• Example
• S30 for 1 8 27 64 125
• Is the series Arithmetic, Geometric, or
  Neither?
• NEITHER!!!!!

8
Sigma Notation

• Look for a pattern for tk
• S30 for 1 8 27 64 125
• tk k3
• So, our answer is

9
Ex Use sigma notation to write the series
10 15 20 100
Arithmetic
d 5
t1 10
tn 10 (n 1)(5)
5n 5
tn 10 5n 5
Find upper limit
(what term is 100)
tn 5n 5
?100 5n 5
? 19 n
10
Ex Use sigma notation to write the series
Series is geometric!!
tn t1 (r)n-1
t1 1
r - 1/3
How did we get r?
Check it!!!
11
Homework

• Pg. 579-581 Q1-10 1 35 odd