  The mean field dynamics of an $N$-particle weekly interacting Boson system
can be described by the nonlinear Hartree equation. In this paper, we present
estimates on the 1/N rate of convergence of many-body Schr\"{o}dinger dynamics
to the one-body nonlinear Hartree dynamics with factorized initial data with
two-body interaction potential $V$ in $L^3 (\mathbb{R}^3)+ L^{\infty}
(\mathbb{R}^3)$.
