1-1/1*2-1/2*3-1/3*4-1/4*5……-1/2008*2009
=1-(1/1*2+1/2*3+1/3*4+1/4*5……+1/2008*2009)
=1-(1-1/2)+(1/2-1/3)+(1/3-1/4)+……+(1/2008-1/2009)
=1-(1-1/2+1/2-1/3+1/3-1/4+……+1/2008-1/2009)
中间正负抵消
=1-(1-1/2009)
=1-2008/2009
=1/2009