Unformatted text preview: a 2 n implies the convergence of X a n n . 5. If ∑ a n converges, and if b n is monotonic and bounded, prove that ∑ a n b n converges. 6. If { E n } n ∈ N is a sequence of closed nonempty and bounded sets in a complete metric space X , if E n +1 ⊂ E n for all n ∈ N , and if lim n →∞ diam E n = 0 , then ∩ ∞ n =1 E n consists of exactly one point. 1...
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This note was uploaded on 12/27/2011 for the course MATH 118a taught by Professor Stopple,j during the Fall '08 term at UCSB.
 Fall '08
 Stopple,J
 Math

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