Unformatted text preview: lim sup n →∞ ( x n + y n ) < lim sup n →∞ x n + lim sup n →∞ y n . (3) Suppose that lim n →∞ y n exists. Prove that lim sup n →∞ ( x n + y n ) = lim sup n →∞ x n + lim n →∞ y n . 4. [10 points] Find lim sup n →∞ x n and lim inf n →∞ x n in the following cases: (1) x n = sin( nπ/ 4). (2) x n = ± 1 + 1 n ² n cos( nπ ) . 5. [10 points] Let x n = sin( n ). Find lim sup n →∞ x n . 1...
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 Spring '09
 Real Numbers, Supremum, Limit of a sequence, Xn, lim sup xn, lim inf xn

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