How to make this 1/2001*2002+1/2002*2003+1/2003*2004

1 / (2001 * 2002) + 1 / (2002 * 2003) = 2003 / (2001 * 2002 * 2003) + 2001 / (2001 * 2002 * 2003) = (2003 + 2001) / (2001 * 2002 * 2003) = (2002 + 2002) / (2001 * 2002 * 2003) = 2 * 2002 / (2001 * 2002 * 2003) = 2 / (2001 * 2003)

2 / (2001 * 2003) + 1 / (2003 * 2004) = (2 * 2004 + 2001) / (2001 * 2003 * 2004) = 3 * 2003 / (2001 * 2003 * 2004) = 3 / 2001 * 2004 = 1 / 667 * 2004

answer: 1 / (667 * 2004)