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Unformatted text preview: Theorem. (b) Show that the union of nitely many compact sets is compact. Problem 4. Prove the n =1 a n is convergent if and only if for any m N n =1 a m + n is convergent. Moreover, n =1 a n converges to a 1 + + a m + n =1 a n + m . Problem 5. (a) State the Monotone Converge Theorem. (b) Dene a 1 = 1 and a n = 31 a n1 for n 2. Determine the convergence or divergence of the sequence ( a n ). 1...
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This note was uploaded on 03/02/2010 for the course MATH 28 taught by Professor Staff during the Spring '08 term at UMass (Amherst).
 Spring '08
 STAFF
 Math

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