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

Is it true that if {pn}{qn}-> 0, that either pn or qn converges to 0?

2. Relevant equations

3. The attempt at a solutionSo far I've made an argument for why it doesn't have to follow (Because we don't know that both sequences converge, and we could have two divergent sequences or a divergent sequence and a convergent sequence whose product converges, for example the alternating harmonic series), However I can't think of any particular counter-example where the product converges to 0.

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# Homework Help: In search of a counter-example

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