  Gravitational radiation can be expressed in terms of an infinite series of
radiative, symmetric trace-free (STF) multipole moments which can be connected
to the behavior of the source. We consider a truncated model for gravitational
radiation from binary systems in which each STF mass and current moment of
order l is given by the lowest-order, Newtonian-like l-pole moment of the
orbiting masses; we neglect post-Newtonian corrections to each STF moment.
Specializing to orbits which are circular (apart from the radiation-induced
inspiral), we find an explicit infinite series for the energy flux in powers of
$v/c$, where v is the orbital velocity. We show that the series converges for
all values $v/c < 2/e$ when one mass is much smaller than the other, and $v/c <
4/e$ for equal masses,where e is the base of natural logarithms. These values
include all physically relevant values for compact binary inspiral. This
convergence cannot indicate whether or not the full series (obtained from the
exact moments) will converge. But if the full series does not converge, our
analysis shows that this failure to converge does not originate from summing
over the Newtonian part of the multipole moments.
