The J=0 many-body Schrodinger equation for He-4(N) clusters with N=3-10 is solved numerically by combining Monte Carlo methods with the adiabatic hyperspherical approximation. We find ground state and excited state energies for these systems with an adiabatic separation scheme that reduces the problem to motion in a one-dimensional effective potential curve as a function of the hyperspherical radius R. We predict the number of J=0 bound states for these clusters, and also the He+HeN-1 elastic scattering lengths up to N=10. For N=5-10, these are the first such calculations reported.