  In 1978, Lubkin proposed a method of approximating the mean von Neumann
entropy for a subsystem of a finite-dimensional quantum system in an overall
pure state by expanding the entropy as a series in terms of the mean trace of
powers of the system's reduced density operator, but the convergence of this
series was never established. We find an exact closed form expression for the
mean traces, which enables us to prove that the series converges if and only if
the system's dimension $m\le2$, in spite of the fact that Lubkin's proposed
approximation for the entropy is now known to be correct.
