easy example, put
Give examples to show that if and both diverge, then each of the series and may converge or diverge.
I'm not 100% sure how to complete this, though I was advised to use , which is divergent. I'm not quite sure how to use this, though.
I think for the first one, if I have , then I can show it is convergent since . This could also work for the second one if I just have .
I've probably got better answers than I think I do, but I could use a second opinion in any case.