# Homework Help: Proof question

1. Jan 26, 2008

### real analyst

1. The problem statement, all variables and given/known data

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

2. Relevant equations

There are none, they can be any sequences I guess

3. The attempt at a solution

I've tried alot of possibilities. My first guess would be a series times it reciprocal, but that just gives every term to be one, so, I dont know if thats 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 dont think thats 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.
1. The problem statement, all variables and given/known data

2. Relevant equations

3. The attempt at a solution

2. Jan 26, 2008

### ircdan

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