We estimate the acceleration on the Local Group (LG) from the 2 Micron All-Sky Redshift Survey (2MRS). The sample used includes about 23 200 galaxies with extinction-corrected magnitudes brighter than K(s)= 11.25 and it allows us to calculate the flux-weighted dipole. 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. This is combined with the redshift information to determine the change in dipole with distance. The misalignment angle between the LG and the cosmic microwave background (CMB) dipole drops to 12 degrees +/- 7 degrees at around 50 h(-1) Mpc, but then increases at larger distances, reaching 21 degrees +/- 8 degrees at around 130 h(-1) Mpc. Exclusion of the galaxies Maffei 1, Maffei 2, Dwingeloo 1, IC342 and M87 brings the resultant flux dipole to 14 degrees +/- 7 degrees away from the CMB velocity dipole. In both cases, the dipole seemingly converges by 60 h(-1) Mpc. 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(0.6)(m)/b(L)= 0.40 +/- 0.09.