Using ratio test to test conditional convergence?

[theBEAST]

Homework Statement

So what I was taught was that if the lim of the ratio test is the series is always absolutely convergent. If it is >1 the series is always divergent. But if it is =1 then we don't know. So would that mean that all conditionally convergent series would have a limit = 1? I am confused :s

Thanks!

 

[Dick]

Yes, if the ratio test applied to conditional convergent series exists, then it must be 1. On the other hand, the ratio test might not give you a limit at all. In that case the series can do anything it wants to.