Thursday, 2 February 2017

limits - does limNtoinftyfracsumNi=1aisumNi=1bi converge to limNtoinftyfrac1NsumNi=1fracaibi

Can this ever be the case?
limNNi=1aiNi=1bi=limN1NNi=1aibi

with ai>0, bi>0, $a_iothers pointed out simulations indicate convergence, but is there formal ground to it?

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