I heard that there are semi-rigorous arguments that the sum of all (renormalized) terms in QED or QCD perturbation expansions do not converge, even though each term in the sum is systematically renormalized and rendered finite. This is suspected to be the case even if the coupling constant is weak. In other words even though we have fantastic experimental agreement for the electron (g-2) calculated through two loops, the agreement will get worse if could calculate a thousand loops. So, I am looking for references where this is proven, or at least discussed in detail. I searched the forums and could not find a previous discussion on this topic.