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110quiz7solutions

110quiz7solutions - Math 110 Quiz 7 Nov 16 2006 Solutions 1...

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Math 110 Quiz 7 Nov. 16, 2006 Solutions 1) (a) List the first four terms of the sequence with n th term given by a n = ( - 1) n +1 (4 n + 1). (b) List the first four terms of the sequence with a 1 = 1 2 and n th term given recursively by a n = 1 a n - 1 2 for n = 2 , 3 , 4 , . . . Solutions: (a) 5 , - 9 , 13 , - 17 (b) 1 2 , 4 , 1 16 , 256 2) For the following sequences, find the most evident expression for the n th term a n . (a) 3 , 7 , 11 , 15 , . . . (b) 1 2 , - 8 3 , 27 4 , - 64 5 , . . . Solutions: (a) a n = 4 n - 1 (b) ( - 1) n +1 n 3 n + 1 1
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3. What does the sequence given by a n = 3 n n +2 approach as n → ∞ ? Solution: As n → ∞ , this sequence gets closer and closer to 3 Another way to see this is that the function f ( x ) = 3
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