已知|x-2|+(y-4)^2=0求1/xy+1/(x+2)(y+2)+……1/(x+1994)(y+1994)的值

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已知|x-2|+(y-4)^2=0求1/xy+1/(x+2)(y+2)+……1/(x+1994)(y+1994)的值

已知|x-2|+(y-4)^2=0求1/xy+1/(x+2)(y+2)+……1/(x+1994)(y+1994)的值
已知|x-2|+(y-4)^2=0求1/xy+1/(x+2)(y+2)+……1/(x+1994)(y+1994)的值

已知|x-2|+(y-4)^2=0求1/xy+1/(x+2)(y+2)+……1/(x+1994)(y+1994)的值
|x-2|+(y-4)^2=0
|x-2|>=0
(y-4)^2>=0
therefore,
x-2=y-4=0,so x=2,y=4
1/xy+1/(x+2)(y+2)+……1/(x+1994)(y+1994)
= 1/(2*4) + 1/(4*6) + ...+ 1/(1996*1998)
= (1/2)(1/2-1/4+1/4-1/6+...+1/1996-1/1998)
= (1/2)(1/2 - 1/1998)
= 499/1998