Give examples to show that the following series may converge or diverge

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.