Is there a residually finite group not finitely presented? I am looking for a residually finite group which is not finitely presented. Does such a group exist?

$G =\displaystyle\prod_{i\in I} \mathbb{Z}_2$ is not finitely generated (hence not finitely presented) whenever $I$ is infinite. Using projection homomorphisms you can show $G$ to be residually finite.
I can't think of an easy answer for finitely generated groups, but a look at the result in this paper towards the bottom of page 4 shows that that the Lamplighter Group should work.
