由|x-1|+|y-2|=0得x=1,y=2
1/xy+1/(x+1)(y+1)+1/(x+2)(y+2)+.+1/(x+2009)(y+2009)
=1/(1*2)+1/(2*3)+1/(3*4) )+.+1/(2010*2011)
=(1-1/2)+(1/2-1/3)+(1/3+1/4) +.+(1/2010-1/2011)
=1-1/2+1/2-1/3+1/3+1/4 +.+1/2010-1/2011
=1-1/2011
=2010/2011