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单词 Raabe's Test
释义

Raabe's Test

Given a Series of Positive terms and a Sequence of Positive constants , use Kummer's Test


with , giving
 
  

Defining


then gives Raabe's test:
1. If , the Series Converges.

2. If , the Series Diverges.

3. If , the Series may Converge or Diverge.

See also Convergent Series, Convergence Tests, Divergent Series, Kummer's Test


References

Arfken, G. Mathematical Methods for Physicists, 3rd ed. Orlando, FL: Academic Press, pp. 286-287, 1985.

Bromwich, T. J. I'a and MacRobert, T. M. An Introduction to the Theory of Infinite Series, 3rd ed. New York: Chelsea, p. 39, 1991.


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