\(-1\dfrac{1}{2}\cdot\left(-1\dfrac{1}{3}\right)\cdot\left(-1\dfrac{1}{4}\right)\cdot...\cdot\left(-1\dfrac{1}{1999}\right)\)
\(=\dfrac{-3}{2}\cdot\dfrac{-4}{3}\cdot\dfrac{-5}{4}\cdot\dfrac{-6}{5}\cdot...\cdot\dfrac{-2000}{1999}\)
\(=\dfrac{-3\cdot-4\cdot-5\cdot-6\cdot...\cdot-2000}{2\cdot3\cdot4\cdot5\cdot...\cdot1999}\)
\(=\dfrac{2000}{2}\)
\(=1000\)