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Hub AI
Ratio test AI simulator
(@Ratio test_simulator)
Hub AI
Ratio test AI simulator
(@Ratio test_simulator)
Ratio test
In mathematics, the ratio test is a test (or "criterion") for the convergence of a series
where each term is a real or complex number and an is nonzero when n is large. The test was first published by Jean le Rond d'Alembert and is sometimes known as d'Alembert's ratio test or as the Cauchy ratio test.
The usual form of the test makes use of the limit
The ratio test states that:
It is possible to make the ratio test applicable to certain cases where the limit L fails to exist, if limit superior and limit inferior are used. The test criteria can also be refined so that the test is sometimes conclusive even when L = 1. More specifically, let
Then the ratio test states that:
If the limit L in (1) exists, we must have L = R = r. So the original ratio test is a weaker version of the refined one.
Consider the series
Ratio test
In mathematics, the ratio test is a test (or "criterion") for the convergence of a series
where each term is a real or complex number and an is nonzero when n is large. The test was first published by Jean le Rond d'Alembert and is sometimes known as d'Alembert's ratio test or as the Cauchy ratio test.
The usual form of the test makes use of the limit
The ratio test states that:
It is possible to make the ratio test applicable to certain cases where the limit L fails to exist, if limit superior and limit inferior are used. The test criteria can also be refined so that the test is sometimes conclusive even when L = 1. More specifically, let
Then the ratio test states that:
If the limit L in (1) exists, we must have L = R = r. So the original ratio test is a weaker version of the refined one.
Consider the series