Assume the exact result is $\tilde{x}$ and that we are using an RKM method. Suppose we run two calculations, one with $h$ (called $x_1$) and one with $h/2$ (called $x_2$). Then

$$\tilde{x}=x_1+Ch^{M+1}+O(h^{M+2}),$$ and $$\tilde{x}=x_2+2C(h/2)^{M+1}+O(h^{M+2}),$$ with $C$ a constant. Note that we calculate two halves in the last equation. We get then $$|x_1-x_2| = Ch^{M+1}(1-\frac{1}{2^M}).$$ yielding $$C=\frac{|x_1-x_2|}{(1-2^{-M})h^{M+1}}.$$ We rewrite $$\tilde{x}=x_2+\epsilon+O((h)^{M+2}),$$ with $$\epsilon = \frac{|x_1-x_2|}{2^M-1}.$$