Let be a series with Positive terms and let be the function that results when is replaced by
in the Formula for . If is decreasing and continuous for and

then

and

both converge or diverge, where . The test is also called the Cauchy Integral Test or Maclaurin Integral Test.

**References**

Arfken, G. *Mathematical Methods for Physicists, 3rd ed.* Orlando, FL: Academic Press, pp. 283-284, 1985.

© 1996-9

1999-05-26