So when | one |

When |a| >e, the original series diverges.

When a = e, a (n+1)/an = e/(1+1n) n >1,an does not tend to 0;

When a =-e, | a (n+1)/an | = e/(1+1n) n >1,|an| does not tend to 0.

An does not tend to 0, and the series diverges.

To sum up, | a | < E, the series is absolutely convergent;

| a | >； =e, the series diverges.