abstract: Formal power series naturally arise when considering dynamical systems with small divisors problems in the perturbative setting. I will focus on the following examples: lower-dimensional tori in quasi-integrable systems and quasi-periodic solutions in strongly damped one-dimensional systems in the presence of a quasi-periodic forcing. The formal power series in the perturbation parameter can be given a meaning by a suitable summation rule. This leads to quasi-periodic solutions analytic in a domain tangent to the origin. In certain cases the summation rule can be proved to correspond to Borel summability.