1×4分之1+4×7分之1+7×10分之1+……+2002×2005分之1+2005×2008分之1
=(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
1×4分之1+4×7分之1+7×10分之1+……+2002×2005分之1+2005×2008分之1
=(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