x(1/1*2 + 1/2*3 + ...+ 1/2002*2003) = 2002
x(1-1/2 + 1/2 -1/3 + ...+ 1/2002 - 1/2003) = 2002
x(1-1/2003) = 2002
2002*x/2003 = 2002
x = 2003