I was asked to show an s-stage explicit Runge-Kutta Method cannot obtain accuracy higher than $s$. It suffices to consider autonomous system $y' = f(y)$ (otherwise by introducing a new variable $t$, we can re-construct an autonomous system of ODE).
The situation for $s=2$ is easy by direct calculation and comparison with terms in the Taylor expansion. However, for general $s$, expanding the Taylor expansion would be highly complicated. I don't know how to proceed the calculations. Any help would be appreciated.