=1/(x+1)-1/(x+2)+1/(x+2)-1/(x+3)+1/(x+3)-1/(x+4)+1/(x+4)-1/(x+5)...+1/(x+1998)-1/(x+1999)+1/(x+1999)-1/(x+2000) =1/(x+1)-1/(x+2000) =1999/(x+1)(x+2000) =1999/(x^2+2001x+2000)