A general method for estimating fluorescence resonance energy transfer between distributions of donors and acceptors on surfaces is presented. Continued fraction approximants are obtained from equivalent power series expansions of the change in quantum yield in terms of the fluorescent lifetimes or the steady-state fluorescence. These approximants provide analytic equations for the analysis of energy transfer and error bounds for the approximants. Specific approximants are derived for five models of interest for membrane biochemistry: (a) an infinite plane, (b) parallel infinite planes, (c) the surface of a sphere, (d) the surfaces of concentric spheres, and (e) the surfaces of two separated spheres. Recent experimental results in the literature are analyzed with the equations obtained.