Geodesic
A Generalized Comparison Test
Canadian mathematical bulletin, Tome 24 (1981) no. 4, pp. 485-487

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Let ∑ cj and ∑dj be, respectively, convergent and divergent series of positive terms and let ∑ aj be a third series of positive terms. It is well known, [1, pg. 275] that ∑ aj converges if lim sup(aj/cj)<+∞, but diverges if liminf(aj/dj)>0. In this note we prove a generalized version of this comparison test that relies not on term-by-term comparison of the series, but on the relative densities of the terms of the series. 
Johnston, Elgin. A Generalized Comparison Test. Canadian mathematical bulletin, Tome 24 (1981) no. 4, pp. 485-487. doi: 10.4153/CMB-1981-072-0
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     title = {A {Generalized} {Comparison} {Test}},
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