  We propose a generalization of Grunberg's method of effective charges in
which, starting with the effective charge for some dimensionless QCD observable
dependent on the single energy scale $Q, R(Q)$, we introduce an infinite set of
auxiliary effective charges, each one describing the sub-asymptotic Q-evolution
of the immediately preceding effective charge. The corresponding infinite set
of coupled integrated effective charge beta-function equations may be
truncated. The resulting approximations for $R(Q)$ are the convergents of a
continued function. They are manifestly RS-invariant and converge to a limit
equal to the Borel sum of the standard asymptotic perturbation series in
$\alpha_s({\mu^2})$, with remaining ambiguities due to infra-red renormalons.
There are close connections with Pad{\'e} approximation.
