1/1*4+1/4*7+1/7*10+.1/2002*2005+1/2005*2008
=（1-1/4+1/4-1/7+1/7-1/10+……+1/2002-1/2005+1/2005-1/2008）÷3
=（1-1/2008）÷3
=2007/2008÷3
=669/2008