Sum[c[n]r^(2-n/2)+d[n]r^(-n/2),{n,Infinity}]

(* your exclusion conditions *)
conds={2-n/2<0, (* possibly more *) };

filter[c_]:=Piecewise[{{1,And@@c}},0]

Sum[filter[conds] c[n]r^(2-n/2) + filter[conds] d[n]r^(-n/2),{n,Infinity}]