I was asked to show that 2n is divergent. Here is what i did, i assumed that it was convergent and used the fact that a convergent sequence needs to be bounded. let M be the upper bound ,then 2n < M for all natural numbers, then this implies that n < logM/log2 for all natural numbers, which contradicts the Archimedian property. So is this right?
Also i am asked to give two divergent sequences whose product is convergent, i saw an example in this very own site (-1)n and (-1)n+1 are two divergent sequences whose product is convergent. Can u give me some more examples?