2/(1*2*3)=1/(1*2)-1/(2*3)
2/(2*3*4)=1/(2*3)-1/(3*4)
2/(3*4*5)=1/(3*4)-1/(4*5)
…………
2/(1999*2000*2001)=1/(1999*2000)-1/(2000*2001)
原式=1/(1*2)-1/(2*3)+1/(2*3)-1/(3*4)+1/(3*4)-1/(4*5)+……+1/(1999*2000)-1/(2000*2001)
=1/(1*2)-1/(2000*2001)
=2000999/4002000