  Motivated by the recent 4-loop analysis of the JLab data on Bjorken Sum Rule,
where the pQCD series seems to blow up at $|Q|\lesssim 1.5\,\GeV, \alpha_s
\gtrsim 0.33\,,$ we overview the general origin of the divergency of common
perturbation expansion over powers of a small coupling parameter in QFT and
consider in detail the {\it blowing-up phenomenon} and accuracy of finite sums
for simple alternating and non-alternating examples of divergent series.
