Given a Series of Positive terms and a sequence of finite Positive constants , let

- 1. If , the series converges.
- 2. If , the series diverges.
- 3. If , the series may converge or diverge.

**References**

Arfken, G. *Mathematical Methods for Physicists, 3rd ed.* Orlando, FL: Academic Press, pp. 285-286, 1985.

Jingcheng, T. ``Kummer's Test Gives Characterizations for Convergence or Divergence of All Series.''
*Amer. Math. Monthly* **101**, 450-452, 1994.

Samelson, H. ``More on Kummer's Test.'' *Amer. Math. Monthly* **102**, 817-818, 1995.

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1999-05-26