  First it is shown that the tree amplitude for pion pion scattering in the
minimal linear sigma model has an exact expression which is proportional to a
geometric series in the quantity (s-$m_\pi^2$)/($m_B^2-m_\pi^2$), where $m_B$
is the sigma mass which appears in the Lagrangian and is the only a priori
unknown parameter in the model. This induces an infinite series for every
predicted scattering length in which each term corresponds to a given order in
the chiral perturbation theory counting.
  It is noted that, perhaps surprisingly, the pattern, though not the exact
values, of chiral perturbation theory predictions for both the isotopic spin 0
and isotopic spin 2 s-wave pion-pion scattering lengths to orders $p^2$, $p^4$
and $p^6$ seems to agree with this induced pattern. The values of the $p^8$
terms are also given for comparison with a possible future chiral perturation
theory calculation. Further aspects of this approach and future directions are
briefly discussed.
