x-2的绝对值+y-4的绝对值=0,求xy/1+(x+2)(y+2)/1+(x+4)(y+4)/1+...+(x+2010)(y+2010)/1

由|x-2|+|y-4|=0,得x=2,y=4,
所以原式=1/(2×4)+1/(4×6)+1/(6×8)+…+1/(2012×2014)
=(1/2)[(1/2-1/4)+(1/4-1/6)+(1/6-1/8)+…+(1/2012-1/2014)]
=(1/2)(1/2--1/2014)=(1/2)(1006/2014)=503/2014.