Proving Convergence of Sum/Product of Non-Convergent Sequences

[real analyst]

Homework Statement

Prove by an example that the sum or product of two non convergent sequences can be convergent

Homework Equations

There are none, they can be any sequences I guess

The Attempt at a Solution

I've tried a lot of possibilities. My first guess would be a series times it reciprocal, but that just gives every term to be one, so, I don't know if that's really a good example. I also tried adding a sequence to i'ts negative sequence, but, that o course gives zero for every term. I don't think that's what he's looking for either. I also tried adding a function that goes to infinity to a function that goes to negative function, but I found that one function always outweighs the other, Any help would be appreciated.

 

[ircdan]

well I'm sure you've shown that a_n = (-1)^n doesn't converge, now what's a_na_n?