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Unformatted text preview: ∞ X n =1 1 n 2 = π 2 6 . Evaluate ∞ X n =1 1 (2 n1) 2 , and ∞ X n =1 (1) n 1 n 2 . 5. Call a mapping of X into Y open if f ( V ) is an open set in Y whenever X is an open set in X . Prove that every continuous open mapping from R into R is monotonic. 6. Consider a sequence of positive numbers { a n } such that a n + m ≤ a n + a m ∀ n, m ≥ . Prove that lim n →∞ a n n exists. 7. Evaluate the following limit directly: lim x → a x na n xa , for n ∈ N ....
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 Fall '08
 Stopple,J
 Math, Topology, Open set, Topological space, continuous open mapping

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