  In 1952 Dyson put forward a simple and powerful argument indicating that the
perturbative expansions of QED are asymptotic. His argument can be related to
Chandrasekhar's limit on the mass of a star for stability against gravitational
collapse. Combining these two arguments we estimate the optimal number of terms
of the QED series to be 3.1(137)^{3/2}=5000.
