Determine bounded sequence of positive real number

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Reference no: EM13204294

Let(bn)be a bounded sequence of positive real number such that for any bounded positive sequence of real number we have:
limsup(an bn)= limsup(an)limsup(bn). Prove (bn) is convergent sequence or on the other hand: I am having a hard time to solve this problem please help.

lim n->infinity bn/an=0 Here how can i find a sequence an and a sequence bn without using Ratio Test. The Limit above is true and the Ratio Test gives no conclusion about the convergence of either "sigma an or sigma bn" even though sigma bn is much smaller than the terms of sigma bn.

Reference no: EM13204294

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