  We present the construction of a gravitational action including an infinite
series of higher derivative terms. The outcome is a classically consistent
completion of a well-studied quadratic curvature theory. The closed form for
the full action is ghost-free bimetric theory, describing the interactions of a
massive and a massless spin-2 field. At energies much smaller than the spin-2
mass scale, the theory reduces to general relativity. For energies comparable
to the spin-2 mass, the higher derivative terms completing the Einstein-Hilbert
action capture the effects of the additional massive spin-2 field. The theory
is only ghost-free when the full series of higher derivatives is kept.
