Right.  I tried that, but I found that it didn't work out nearly as well. I couldn't get good convergence with just the 2nd term when I used F(k) ~= 1/k^2 (a + b k^-1/n).  It was much better with F(k) ~= 1/k^2 (a + b/k) for deVaucouleurs in particular (where the difference in the two functional forms is largest).