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so they are non-negative and bounded. how do i show this?

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I think that $x_n=1+\sin(n)$, $y_n=1+\cos(n)$ work. The limsup of the product is less than 3. The limsup of each separately is 2, so the product is 4.

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that makes sense. thank you! –  Dafty Oct 10 '13 at 23:31

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