1/ab+1/(a-1)(b-1)+1/(a-2)(b-2)+.+1/(a-2009)(b-2009)的值
=1/(-1)(-2)+1/(-2)(-3)+(-3)(-4)+……+1/(-2010)(-2011)
=1/1-1/2+1/2-1/3+1/3-1/4+……+1/2010-1/2011
=1-(1/2011)
=2010/2011