It is known that the absolute value of XY-2 is opposite to that of Y-1 Try to find the value of 1 + (x + 1) (y + 1) of XY + (x + 2) (y + 2) of XY +... + (x + 2014) (y + 2014) of XY

It is known that the absolute value of XY-2 is opposite to that of Y-1 Try to find the value of 1 + (x + 1) (y + 1) of XY + (x + 2) (y + 2) of XY +... + (x + 2014) (y + 2014) of XY

Solution: ∵ XY-2 ∵ Y-1 ∵ Y-1 = 0, that is, y = 1; XY-2 = 0, X * 1-2 = 0, x = 2. Then 2 / XY + 2 / (x + 1) (y + 1) + 2 / (x + 2) (y + 2) + +2/(x+2012)(y+2012)=2/(1x2)+2/(2x3)+2/(3x4)+… +2/(2013x2014)=2x[1/(1x2)+1/(2x3)+1/(3x4)+… +1/(2013x2014)]=...