Question

\(\frac{-1}{2000\times1999}-\frac{1}{1999\times1998}-\frac{1}{1998\times1997}\)

Answer 1

\(\frac{-1}{2000\cdot1999}-\frac{1}{1999\cdot1998}-\frac{1}{1998\cdot1997}\)

\(=-\left(\frac{1}{2000\cdot1999}+\frac{1}{1999\cdot1998}+\frac{1}{1998\cdot1997}\right)\)

\(=-\left(\frac{1}{1997\cdot1998}+\frac{1}{1998\cdot1999}+\frac{1}{1999\cdot2000}\right)\)

\(=-\left(\frac{1}{1997}-\frac{1}{1998}+\frac{1}{1998}-\frac{1}{1999}+\frac{1}{1999}-\frac{1}{2000}\right)\)

\(=-\left(\frac{1}{1997}-\frac{1}{2000}\right)\)

\(=-\frac{3}{3994000}\)