The ratio test, also called d'Alembert's criterion, examines a series 
with positive
terms through the limit
Then
1. If 
, the series converges.
2. If 
or 
, the series diverges.
3. If 
, the series
may converge or diverge.
The test is also called the Cauchy ratio test or d'Alembert ratio test.
See also
Convergence Tests Explore this topic in the MathWorld classroom
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References
Arfken, G. Mathematical Methods for Physicists, 3rd ed. Orlando, FL: Academic Press, pp. 282-283,
1985.Bromwich, T. J. I'A. and MacRobert, T. M. An
Introduction to the Theory of Infinite Series, 3rd ed. New York: Chelsea,
p. 28, 1991.Zwillinger, D. (Ed.). "Convergence Tests."
§1.3.3 in CRC
Standard Mathematical Tables and Formulae, 30th ed. Boca Raton, FL: CRC Press,
p. 32, 1996.Referenced on Wolfram|Alpha
Ratio Test
Cite this as:
Weisstein, Eric W. "Ratio Test." From
MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/RatioTest.html
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