14. Let the larger root of the equation $2002^{2} x^{2}-2003 \times 2001 x-1=0$ be $r$, and the smaller root of the equation $2001 x^{2}-2002 x+1=0$ be $s$. Find the value of $r-s$.
14. Since $2002^{2} x^{2}-2003 \times 2001 x-1=0$, the two roots are
$$
x_{1}=1, x_{2}=-\frac{1}{2002^{2}} \text {. }
$$

Therefore, $r=x_{1}=1$.
Similarly, the two roots of the equation $2001 x^{2}-2002 x+1=0$ are $x_{1}=1, x_{2}=\frac{1}{2001}$.
Thus, $s=x_{2}=\frac{1}{2001}$.
Hence, $r-s=1-\frac{1}{2001}=\frac{2000}{2001}$.