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We determine the gravitational response to a diffuse source, in a locally deSitter background, of a class of theories which modify the Einstein-Hilbertaction by adding a term proportional to an inverse power of the Ricci scalar.We find a linearly growing force which is not phenomenologically acceptable.Comment: 10 pages, LaTeX 2 epsilon, no figures. Minor conceptual change

Letter: The Force of Gravity from a Lagrangian Containing Inverse Powers of the Ricci Scalar