Example of two variable limit with special instruction on iterated limits

Question

So, here is a question about two-variable-limit and iterated limits that needs an example.

Giving a doubly indexed array $a_{mn}$ where $m,n \in \Bbb N$.
Then construct an example where lim$_{m,n\rightarrow\infty}$ $a_{mn}$ exists but neither the iterated could be computed.

I have a basic idea if it was asking lim$_{m,n\rightarrow(0,0)}$, but now I'm stuck with this question.

Answer 1

What about $$a_{mn}=\frac{(-1)^m}{n}+\frac{(-1)^n}{m}.$$