1\(a*b)=1\a-1\b
故上式1\(2×3)+1\(3×4)+1\(4×5)+…+1\(1000×1001)
=1\2-1\3+1\3-1\4+1\4+1\5-……+1\1000-1\1001
=1\2-1\1001
=999/2002