## Kummer's Test

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.

The test is a general case of Bertrand's Test, the Root Test, Gauss's Test, and Raabe's Test. With and , the test becomes Raabe's Test.

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.