($\frac{1}{2}$ - 1)($\frac{1}{3}$ - 1 )....($\frac{1}{1999}$ - 1 )
= $\frac{-1}{2}$ . $\frac{-2}{3}$ ..... $\frac{-1998}{1999}$
= - ( $\frac{1}{2}$ . $\frac{2}{3}$ ..... $\frac{1998}{1999}$ )
= - ( $\frac{1}{1999}$ )
= $\frac{-1}{1999}$
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