[0DY](Proposed on 2022-12-13) Find two sequences \((a_ n)_ n,(b_ n)_ n\) with \(a_ n,b_ n{\gt}0\) such that \(β_{n=0}^β (-1)^ n a_ n\) is convergent, \(β_{n=0}^β (-1)^ n b_ n\) is non-convergent, and \(\lim _{nββ} a_ n/b_ n=1\).
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