  We consider the evolution of N bosons, where N is large, with two-body
interactions of the form $N^{3\beta}v(N^\beta \cdot)$, $0\leq\beta\leq 1$. The
parameter $\beta$ measures the strength of interactions. We compare the exact
evolution with an approximation which considers the evolution of a mean field
coupled with an appropriate description of pair excitations, see Commun. Math.
Phys. 294: 273-301, 2010 and Adv. Math. 228: 1788-1815, 2011. For $0\leq\beta <
1/2$, we derive an error bound of the form $p(t)/N^\alpha$, where $\alpha > 0$
and $p(t)$ is a polynomial, which implies a specific rate of convergence as
$N\rightarrow\infty$.
