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Unformatted text preview: x n is a convergent sequence of nonnegative numbers with limit L , then x n is a convergent sequence with limit L .] 4. Same question for c n given by c 1 = 1 and c n +1 = 1 1+ c n for n > 1. [Justify your calculation using the theorems from April 2.] 5. Dene the sequence a n by a 1 = 2 and a n +1 = 2 a n +2 a n +2 for n > 1. It might help to do 5(c) rst. 5(a). Prove that the sequence a n is bounded. (If you are starting this homework before I have dened it in class: exhibit a number B and a proof that | a n | B for all n N .) 5(b). Prove that the sequence a n is decreasing. (If you are starting this homework before I have dened it in class: prove that a n-a n +1 > 0 for all n . 5(c). If the sequence converges to a limit, what is the limit? 1...
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This homework help was uploaded on 04/02/2008 for the course MATH 74 taught by Professor Courtney during the Fall '07 term at University of California, Berkeley.
- Fall '07