  The exact mass gap of the O(N) Gross-Neveu model is known, for arbitrary $N$,
from non-perturbative methods. However, a "naive" perturbative expansion of the
pole mass exhibits an infinite set of infrared renormalons at order 1/N,
formally similar to the QCD heavy quark pole mass renormalons, potentially
leading to large ${\cal O}(\Lambda)$ perturbative ambiguities. We examine the
precise vanishing mechanism of such infrared renormalons, which avoids this
(only apparent)contradiction, and operates without need of (Borel) summation
contour prescription, usually preventing unambiguous separation of perturbative
contributions. As a consequence we stress the direct Borel summability of the
(1/N) perturbative expansion of the mass gap. We briefly speculate on a
possible similar behaviour of analogous non-perturbative QCD quantities.
