a/(a+2001) + 2b/(2b+2001) + 3c/(3c+2001) =
= (a+2001-2001)/(a+2001) + (2b+2001-2001)/(2b+2001) + (3c+2001-2001)/(3c+2001) =
= (1 +1+1) - 2001(1/(a+2001)+1/(2b+2001)+1/(3c+2001)) =
= 3 - 2001*3/2002 = (2002*3-2001*3)/2002 = (2002-2001)*3/2002 = 3/2002
