1x2分之1+2X3分之1+3X4分之1+.+2007X2008分之1+12008X2009分之1
=1-(1/2)+(1/2)-(1/3)+(1/3)-(1/4)+...+(1/2007)-(1/2008)+(1/2008)-(1/2009)
=1-(1/2009)
=2008/2009