  We estimate the flux weighted acceleration on the Local Group (LG) from the
near-infrared Two Micron All Sky Redshift Survey (2MRS). The near-infrared flux
weighted dipoles are very robust because they closely approximate a mass
weighted dipole, bypassing the effects of redshift distortions and require no
preferred reference frame. We use this method with the redshift information to
determine the change in dipole with distance. The LG dipole seemingly converges
by 60 Mpc/h. Assuming convergence, the comparison of the 2MRS flux dipole and
the CMB dipole provides a value for the combination of the mass density and
luminosity bias parameters Omega_m^0.6/b_L= 0.40+/-0.09.
