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 a n just to notate more clearly we are looking at patterns

Vocabulary Series- The sum of a sequence Notated S n : Means we need to add up the first n terms in a given sequence – Let a n = a 1, a 2, a 3, a 4, …, a n – Then S n = a 1 + a 2 + a 3 + a 4 + …+ a n

Vocabulary Summation Notation(Also called sigma notation) – What we will use to calculate a series- the sum of terms Notation: Read the SUM of the terms in the sequence a n from term in position 1 to the term in position n

aiai aiai Thus we would add up terms in position 1 through 5 = a 1 + a 2 + a 3 + a 4 + a 5

Example Page # 622 #76

Example 2 Page 622 #89

Activity let a n = 3x + 3

Summation Properties Consider a n = 5 a 1 5 a2 5a2 5 a3 5a3 5 a4 5a4 5 a5 5a5 5 a n = ++++

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

Summation Property 2 = 5(1) + 5(2) + 5(3) + 5(4) + 5(5) = 5( ) a n = 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:

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

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