  We demonstrate that in the mass independent renormalization scheme. the
renormalization group equations associated with the unphysical parameters that
characterize the renormalization scheme and the mass scale leads to summation
that results in a cancellation between the implicit and explicit dependence on
these parameters. The resulting perturbative expansion is consequently
independent of these arbitrary parameters. We illustrate this by considering R,
the cross section for e+e- -> hadrons.
