1 / (1 * 4) - 1 / (4 * 7) - 1 / (7 * 10) - 1 / (10 * 13)... - 1 / (2002 * 2005) - 1 / (2005 * 2008)

1 / (1 * 4) - 1 / (4 * 7) - 1 / (7 * 10) - 1 / (10 * 13)... - 1 / (2002 * 2005) - 1 / (2005 * 2008)

(1 / 3) * (1 - 1 / 4 + 1 / 4 - 1 / 7 + 1 / 7 - 1 / 10 + 1 / 10 + 1 / 10 + 1 / 2005 - 1 / 2008
= (1 / 3) * (1 - 1 / 2008)
= 1 / 3 * 2007 / 2008
= 669 / 2008