  We study weak coupling perturbative series in 4d N=2 and 5d N=1
supersymmetric gauge theories with Lagrangians. We prove that the perturbative
series of these theories in zero instanton sector are Borel summable for
various observables. Our result for 4d $\mathcal{N}=2$ case supports an
expectation from a recent proposal on a semiclassical realization of infrared
renormalons in QCD-like theories, where the semiclassical solution does not
exist in N=2 theories and the perturbative series are unambiguous, namely Borel
summable. We also prove that the perturbative series in arbitrary number of
instanton sector are Borel summable for a wide class of theories. It turns out
that exact results can be obtained by summing over the Borel resummations in
each number of instanton sector.
