Chapter 8 (F11)

Chapter 8 (F11) - Section 8.1 Sequences and Summation...

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Section 8.1 – Sequences and Summation Notation A sequence is a function whose domain is the positive integers. ( n = 1, 2, 3, …) The terms of a sequence are the numbers in the sequence and are represented by: a 1 , a 2 , a 3 , …, a n , … The n th term of a sequence is the general (generic) term of the sequence. Examples : 1. Write the first five terms of: { n 2 + 1 } 2. Write the first four terms of: {(–1) n +1 5 n } The factorial symbol n ! is defined as: n ! = n ( n – 1)( n – 2) ∙∙∙3∙2∙1 and 0! = 1 Examples : a) 4! = b) ! 5 ! 8 = 1
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Summation Notation : 1 2 1 n i n i a a a a = = + + + K Examples : Find the following sums: 1. 6 1 ! i i = 2. 4 2 1 1 i i = 3. 3 1 (4 1) i i = - 4. 4 1 ( 1) 3 i i i = - 2
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Section 8.2 – Arithmetic Sequences An arithmetic sequence is one in which each term after the first is obtained by adding a non-zero constant to the preceding term. The constant is called the common difference . Examples
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Chapter 8 (F11) - Section 8.1 Sequences and Summation...

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