I want to find a counter example
This is the Fubini theorem for sequences:
If $$\sum^{\infty}_{n=1}\sum^{\infty}_{m=1}|a_{mn}|<\infty,$$
then
$$\sum^{\infty}_{m=1}\sum^{\infty}_{n=1}a_{mn}=\sum^{\infty}_{n=1}\sum^{\infty}_{m=1}a_{mn}.$$
Then, does there exist a sequence $\{a_{mn}\}$ such that the left and the right hand sides of equality are finite but are not equal?