08_SequencesLimitsStolz
13
When determining the limit of a sequence lim n n n x y →∞ where lim n n x →∞ = ∞ lim n n y →∞ = ∞ the foll owing theorem due to O. Stolz may be used to advant age Let lim n n y →∞ = ∞ and let some index N exist such that 1 n n y y + > whenever n N > . Then 1 1 lim lim n n n n n n n n x x x y y y − →∞ →∞ − − = − provided that the right-hand-side limit exists (finite or infinite)
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