quiz1_sequences_solutions

# quiz1_sequences_solutions - (3) (2 points) Circle the...

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Mathematics 2602 Quiz #1 Solutions January 19, 2006 Let { a n } n = n =1 = 1 - 1 2 n n Let { b n } n = n =1 = ( - 1) n + 3 Let { c n } n = n =1 = 1 - 1 ( - 2) n (1) (2 points) Which of the sequences (if any) are monotone? a n is a decreasing sequence, so it is monotone. b n and c n both oscillate, so are not monotone. (2) (4 points) List each sequence above which converges to a limit and give that limit. lim n →∞ { a n } = 0 (It is bounded below by zero and is decreasing). lim n →∞ { b n } doesn’t exist. lim n →∞ { c n } = 1 (The distance between one and the sequence decreases each time, even though it oscillates above and below it).
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Unformatted text preview: (3) (2 points) Circle the correct answer (a) n 2 = o ( n 3 2 ) (b) n 3 2 = o ( n 2 ) (c) n 2 = ( n 3 2 ) Since 3 2 &lt; 2, we have that n 3 2 = o ( n 2 ). (4) (2 points) Circle the correct answer (a) 2 n = o (2 . 1 n ) (b) 2 . 1 n = o (2 n ) (c) 2 n = (2 . 1 n ) Since both 2 n and 2 . 1 n are exponentials, we just have to compare the size of their bases. since 2 . 1 &gt; 2 we have that 2 n = o (2 . 1 n )....
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## This note was uploaded on 11/08/2009 for the course MATH 2602 taught by Professor Costello during the Spring '09 term at Georgia Institute of Technology.

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