∵|x1-1|+|x2-2|^2+|x3-3|^3+······+|x2000-2000|^2000=0,
∴x1=1、x2=2、x3=3、x4=4、x5=5、······、x2000=2000,
∴1/(x1x2)+1/(x2x3)+1/(x3x4)+1/(x4x5)+······+1/(x1999x2000)
=1/(1×2)+1/(2×3)+1/(3×4)+1/(4×5)+······+1/(1999×2000)
=(1-1/2)+(1/2-1/3)+(1/3-1/4)+(1/4-1/5)+······+(1/1999-1/2000)
=1-1/2000
=1999/2000.