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Beyond the ratio test
Published online by Cambridge University Press: 17 October 2018
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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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