  The linear delta expansion is applied to the 3-dimensional O(N) scalar field
theory at its critical point in a way that is compatible with the large-N
limit. For a range of the arbitrary mass parameter, the linear delta expansion
for <phi^2> converges, with errors decreasing like a power of the order n in
delta. If the principal of minimal sensitivity is used to optimize the
convergence rate, the errors seem to decrease exponentially with n.
