  The perturbative expansion series in coupling constant in QED is divergent.
It is either an asymptotic series or an arrangement of a conditionally
convergent series. The sum of these types of series depends on the way we
arrange partial sums for successive approximations. The $1/N_f$ series
expansion, where $N_f$ is the number of flavours, defines a rearrangement of
this series, and therefore, its convergence would serve as a proof that the
perturbative series is, in fact, conditionallyconvergent.Unfortunately, the
$1/N_f$ series also diverges.We proof this usingarguments similar to those of
Dyson.
  We expect that some of the ideas and techniques discussed in our paper will
find some use in finding the true nature of the perturbative series in coupling
constant as well as the $1/N_f$ expansion series.
