Series

D = 1, the D’Alembert criterion cannot be used for deciding whether the series is convergent or divergent.

4. Cauchy’s criterion. Suppose that there exists the limit (finite or infinite)

an = K.

For K < 1, the series ∞∑

n=1 an is convergent; for K > 1, the series is divergent. For K = 1,

the Cauchy criterion cannot be used to establish convergence of a series.