9.1 Series

Objectives:Understand Notation!! Reading the language and symbols which ask you to add the terms

of a sequence

Remember

• Sequences are function- We use an equation to represent a sequence pattern

• We used to use f(n), but we use an just to notate more clearly we are looking at patterns

Vocabulary

• Series- The sum of a sequenceNotated Sn : Means we need to add up the first n terms in a given sequence

– Let an = a1 , a2 , a3 , a4 , …, an

– Then Sn = a1 + a2 + a3 + a4 + …+ an

Vocabulary• Summation Notation(Also called sigma notation)– What we will use to calculate a series- the sum of

terms

n

iia

1

Notation: Read the SUM of the terms in the sequence an from term in position 1 to the term in position n

ai

ai

Thus we would add up terms in position 1 through 5

= a1 + a2 + a3 + a4 + a5

Example

Page # 622 #76

Example 2

• Page 622 #89

Activity let an = 3x + 3

Summation Properties

• Consider

5

1

5i

an = 5

a1

5

a2

5

a3

5

a4

5

a5

5

an =

5

1ina + + + +

Property 1:The summation of a sequence given by a constant (c is a constant)

n

i

c1

cn

Summation Property 2

= 5(1) + 5(2) + 5(3) + 5(4) + 5(5)

ii

5

1

5

= 5(1 + 2 + 3 + 4 + 5 )

an = 5n

Property 2:The summation of a sequence given by a scalar multiple (c is a constant scalar)

Pull out the constant and find the sum

Example:

n

iica

1

26

3

2ii

n

iiac

1

Property 3:Summation of polynomials (addition/subtraction of many terms)

iii

23

1

)]3()3[()]2()2[()]1()1[( 222

)3()3()2()2()1()1( 222

)3()2()1()3()2()1( 222

nnan 2

Property 3:Summation of polynomials (addition/subtraction of many terms)

)(1

n

n

in ba

n

in

n

in ba

11

• Page 622 #71-79; 83; 87-90; 105; 106; WS