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Unformatted text preview: lim x n 6 = 0 ? Give a counterexample. 3. The sequence ( x n ) satis&es the following condition: for every positive integer n;k with n ± k 2 ; we have j x n j < 1 2 k : Find one (speci&c) integer m so that j x m j < 1 999 . Prove your answer. 4. Suppose ( x n ) is a convergent : (a) If x n > for all n; is it always true that lim x n > 0? Can you &nd a counterexample? (b) If lim x n 2 [0 ; 1] ; Show that the set A = & k : ± ± x k & 1 2 ± ± > 3 5 ² is &nite. 1...
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This note was uploaded on 06/25/2010 for the course MATH MATH 301 taught by Professor Alberterkip during the Fall '08 term at Sabancı University.
- Fall '08