To be honest, I don't really understand this exercise in the first place.
A numerical method is convergent only if it is consistent, so what is even the point of a non-consistent numerical method if it isn't convergent in the first place?
Anyways, how should I prove this? I thought about writing out:
$$r_k (h) = x(t_{k+1}) - x(t_k) - h \Psi_f (h, t_k, x_k, x_{k+1})$$
by expanding one of the components as a Taylor series (up to $p$ so we get the remainder $\mathcal{O}(h^{p+1})$)
But I don't think that's the way I should do the exercise. I think we should rather just find a neat example of a non-consistent $\Psi_f$, and not try to prove it by direct calculation?