Abstract
D'Alembert's ratio test, a very basic plank in the theory of infinite series, can be stated as follows:Suppose that an > 0 for all n ≥ 1. Then: (i)if for some n0 and some ρ < 1, we have for all n ≥ n0, then is convergent;(ii)if for some n0, we have for all n ≥ n0, then is divergent.
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