  The single renormalon-chain contribution to the correlator of scalar currents
in QCD is calculated in the $\bar{MS}$-scheme in the limit of a large $N_f$. We
find that in the factorial growth of the coefficients due to renormalons takes
over almost immediatelly in the euclidean region. The essential differences
between the large-order growth of coefficients in the scalar case, and in the
vector case are analysed. In the timelike region a stabilization of the
perturbative series for the imaginary part, with $n$-loop behaviour
$S_n/[\log(s/\Lambda^2)]^{n-1}$, where $S_n$ is essential constant for
$n\le{6}$, is observed. Only for $n\ge{7}$ does one discern the factorial
growth and alternations of sign. Out all-order results are used to scrutinize
the performance of multiloop estimates, within the ``naive nonabelianization''
procedure, and the effective charges approach. The asymtotic behaviour of
perturbative coefficients, in both large $N_f$ and large $N_c$ limits, is
analysed. A contour-improved resummation technique in the time-like region is
developed. Some subtleties of scheme-dependence are illustrated using results
in the $\bar{MS}$ and $V$-schemes. The all-order series under investigation are
summed up with the help of the Borel resummation method. The results obtained
are relevant to the analysis of the theoretical uncertainties in the 4-loop
extractions of the running and invariant $s$-quark masses from QCD sum rules,
and in calculations of the Higgs boson decay width into a quark-antiquark pair.
