  Exact large-$N_{f}$ results for the QCD Adler $D$-function and Deep Inelastic
Scattering sum rules are used to resum to all orders the portion of QCD
perturbative coefficients containing the highest power of
$b$=$\frac{1}{6}(11N$--$2N_{f})$, for SU($N$) QCD with $N_{f}$ quark flavours.
These terms correspond to renormalon singularities in the Borel plane and are
expected asymptotically to dominate the coefficients to all orders in the
$1/N_{f}$ expansion. Remarkably, we note that this is already apparent in
comparisons with the exact next-to-leading order (NLO) and next-to-NLO (NNLO)
perturbative coefficients. The ultra-violet ($UV$) and infra-red ($IR$)
renormalon singularities in the Borel transform are isolated and the Borel sum
(principal value regulated for $IR$) performed. Resummed results are also
obtained for the Minkowski quantities related to the $D$-function, the
$e^{+}e^{-}$ $R$-ratio and the analogous $\tau$-lepton decay ratio, $R_{\tau}$.
The renormalization scheme dependence of these partial resummations is
discussed and they are compared with the results from other groups [1--3] and
with exact fixed order perturbation theory at NNLO. Prospects for improving the
resummation by including more exact details of the Borel transform are
considered.
