1. 9.1 Series Objectives: Understand Notation!! Reading the language and symbols which ask you to add the terms of a sequence

2. 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

3. 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

4. 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

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

6. Example Page # 622 #76

7. Example 2 Page 622 #89

8. Activity let a n = 3x + 3

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

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

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

12. 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:

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

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