(1- $\frac{1}{10}$ )×(1- $\frac{1}{11}$ )×(1- $\frac{1}{12}$ )×...×(1- $\frac{1}{2003}$ )
= ( $\frac{10}{10}$ - $\frac{1}{10}$ )×( $\frac{11}{11}$ - $\frac{1}{11}$ )×( $\frac{12}{12}$ - $\frac{1}{12}$ )×...×( $\frac{2003}{2003}$ - $\frac{1}{2003}$ )
= $\frac{9}{10}$ × $\frac{10}{11}$ × $\frac{11}{12}$ × ... × $\frac{2002}{2003}$
= $\frac{9}{2003}$