In the following link:
Examples of dense sets in the complex plane
we can see an example which says that the following function converges:
$$f(x)=\displaystyle\sum_{n=0}^\infty\frac{1}{2^n}\frac{1}{x-r_n}\sin\left(\frac{1}{x-r_n}\right) $$
where $r_n$ is any fixed enumeration of the rational, and $f(r_n)=0$.
Why this expression converges?
