(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Suppose that (x_n) is a properly divergent sequence, and suppose that (x_n) is unbounded above. Suppose that there exists a sequence (y_n) such that limit (x_n * y_n) exists. Prove that (y_n) ===> 0.

2. Relevant equations

(x_n) ===> 0 <====> (1/x_n) ===> 0

3. The attempt at a solution

One can say with certanty that (y_n) must be bounded, as if it weren't, for all K in Naturals, there exists a b_1 in (x_n) > |K| and b_2 > |K|, and there product is unbounded.

If (y_n) is bounded, and does not converge to 0, then... what?

That's where I'm stuck. How do I finish this?

Thanks.

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# Homework Help: Properly Divergent Sequences

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