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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 thepole mass exhibits an infinite set of infrared renormalons at order 1/N,formally similar to the QCD heavy quark pole mass renormalons, potentiallyleading to large ${\cal O}(\Lambda)$ perturbative ambiguities. We examine theprecise vanishing mechanism of such infrared renormalons, which avoids this(only apparent)contradiction, and operates without need of (Borel) summationcontour prescription, usually preventing unambiguous separation of perturbativecontributions. As a consequence we stress the direct Borel summability of the(1/N) perturbative expansion of the mass gap. We briefly speculate on apossible similar behaviour of analogous non-perturbative QCD quantities.Comment: 16 pp., 1 figure. v2: a few paragraphs and one appendix added, title  and abstract slightly changed, essential results unchange

Renormalon cancellation and Borel summability of the Gross-Neveu model mass gap