Unformatted text preview: n →∞ z n = ∞ if and only if lim n →∞ 1 z n = 0 . 5. Show that a complex sequence is unbounded if and only if it has a subsequence which diverges to inﬁnity. 6. Suppose that R is a ﬁxed positive number. Describe the sets on the Riemann sphere which correspond to the following subsets of C : (i) C (0; R ) (ii) C \ D (0; R ) = { z ∈ C :  z  > R } 1...
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 Fall '08
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 lim, Zn, Sivakumar Example Sheet, following geometric series

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