  The effective mass of the quasi-particles in the fermion-Chern-Simons
description of the quantum Hall state at half-filling is computed for
electron-electron interactions $V(r)\sim r^{x-2}$, for $0<x<3/2$, following the
previous work of Stern and Halperin, Phys. Rev. B {\bf 52}, 5890 (1995). The
energy gap of quantum Hall states with filling factors $\nu=\frac{p}{2p+1}$ for
$p\gg 1$ can then be obtained either from the effective mass at half-filling,
as proposed by Halperin, Lee and Read, Phys. Rev. B {\bf 47}, 7312 (1993), or
evaluated directly from the self-energy of the system in presence of the
residual magnetic field; both results are shown to agree as $p\to \infty$. The
energy gap is then given by a self-consistent equation, which asymptotic
solution for $p\gg 1$ and short-range interactions is $E_g(p)\sim
(2p+1)^{-\frac{3-x}{2}}$, in agreement with previous results by Kim, Lee and
Wen, Phys. Rev. B {\bf 52}, 17275 (1995). The power law for the energy gap
seems to be {\it exact} to all orders in the perturbative expansion. Moreover,
the energy gap for systems with Coulomb interaction is recovered in the limit
$x\to 1$.
