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9.1 Series

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

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9.1 Series

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  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 an just to notate more clearly we are looking at patterns

  3. Vocabulary • Series- The sum of a sequence Notated 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

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

  5. ai = a1 + a2 + a3 + a4 + a5 ai Thus we would add up terms in position 1 through 5

  6. Example Page # 622 #76

  7. Example 2 • Page 622 #89

  8. Activity let an = 3x + 3

  9. Summation Properties • Consider an = 5 an = a1 5 a2 5 a3 5 a4 5 a5 5 + + + +

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

  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)

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

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

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