The effective field theory of quantum gravity has been computing, order by order, the coefficients of an infinite series it never summed. We sum it. The series L = R + α₁R² + α₂R³ + ... is a geometric series with ratio −BR, B = ℓ²_P. Its closed form is f(R) = R/(1+BR). All coefficients are fixed simultaneously: αₙ = (−ℓ²_P)^(n-1). No free parameter remains at any order. The same function is derived independently from the Bekenstein-Hawking entropy bound without perturbation theory. Two roads. One destination. The resummation eliminates singularities by construction (R_max = 1/B), removes the cosmological constant problem (f(0) = 0 exactly), and recovers General Relativity exactly when BR ≪ 1. The holographic bound is not a consequence of quantum gravity. It is the principle that closes the series. Four parameter-free falsifiable predictions follow: post-merger gravitational echo delays Δt = F(a/M)·M·ln(M²/B); a massive scalar gravitational-wave mode with m² = c³/6Gℏ; systematic w(z) ≠ −1; and CMB power suppression at l < 10. All fixed by B. All falsifiable now.