Can Asymptotic Series Resolve the Problems of Inflation?

We discuss a cosmological scenario in which inflation is driven by a potential which is motivated by an effective Lagrangian approach to gravity. We exploit the recent arguments \cite{ARZ} that an effective Lagrangian $L_{eff}$ which, by definition, contains operators of arbitrary dimensionality is in general not a convergent but rather an asymptotic series with factorially growing coefficients. This behavior of the effective Lagrangian might be responsible for the resolution of the cosmological constant problem. We argue that the same behavior of the potential gives a natural realization of the inflationary scenario.