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hw5 - = 1 f n = f n-1 f n-2 for n> 2 Consider a sequence...

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CALCULUS 1501 WINTER 2010 HOMEWORK ASSIGNMENT 5. Due February 12. 5.1. Using only the - N definition of convergence of a sequence prove lim n →∞ 2 n + 1 3 n + 2 = 2 3 . 5.2. Determine without proof sup S , the supremum of the set S given by S = n n + m , where n, m N . 5.3. Recall that the Fibonacci sequence is defined by f 1 = f 2 = 1
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Unformatted text preview: = 1 , f n = f n-1 + f n-2 , for n > 2 . Consider a sequence s 1 = 1 , s n = f n +1 f n for n > 1 . Assume that s n converges. Find its limit. 5.4. Let { s n } be defined as s 1 = 0 . 3 , s 2 = 0 . 33 , s 3 = 0 . 333 ,... Prove that { s n } converges. 1...
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