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What is D'Alembert's ratio test?

Updated: 8/17/2019
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15y ago

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D'Alembert's ratio test, or simply the ratio test, is a way of determining whether certain series converge. It goes like this: to check if a series converges, check the sequence of ratios between consecutive terms. If that sequence converges to something less than 1, then the series converges absolutely. If it converges to something greater than 1, or diverges, then the series diverges. If it converges to 1 exactly, then the test is inconclusive.

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Q: What is D'Alembert's ratio test?
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