已知(x-1)^2+(y-2)^2=0,求1/xy+1/(x+1)(y+1)+1/(x+2)(y+2)+……+1/(x+1989)(y+1989)的值

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已知(x-1)^2+(y-2)^2=0,求1/xy+1/(x+1)(y+1)+1/(x+2)(y+2)+……+1/(x+1989)(y+1989)的值
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已知(x-1)^2+(y-2)^2=0,求1/xy+1/(x+1)(y+1)+1/(x+2)(y+2)+……+1/(x+1989)(y+1989)的值
已知(x-1)^2+(y-2)^2=0,求1/xy+1/(x+1)(y+1)+1/(x+2)(y+2)+……+1/(x+1989)(y+1989)的值

已知(x-1)^2+(y-2)^2=0,求1/xy+1/(x+1)(y+1)+1/(x+2)(y+2)+……+1/(x+1989)(y+1989)的值
(x-1)^2+(y-2)^2=0
x-1=0 y-2=0
x=1 y=2
1/xy+1/(x+1)(y+1)+1/(x+2)(y+2)+……+1/(x+1989)(y+1989）
=1/x(x+1)+1/(x+1)(x+2)+1/(x+2)(x+3)+……+1/(x+1989)(x+1990）
=1/x-1/(x+1)+1/(x+1)-1/(x+2)+1/(x+2)-(x+3)+……+1/(x+1989)-1/(x+1990）
=1/x-1/(x+1990）
=1-1/1991
=1990/1991

依题意：x=1，y=2
于是
1/xy+1/(x+1)(y+1)+1/(x+2)(y+2)+……+1/(x+1989)(y+1989)
=1/(1×2)+1/(2×3)+...+1/(1990×1991)
=(1/1-1/2)+(1/2-1/3)+...+(1/1990-1/1991)
=1-1/1991
=1990/1991
完毕

(x-1)^2+(y-2)^2=0
平方和为零 每项均为0
所以
x-1=0 y-2=0
x=1 y=2
后面代入1和2 按他们回答的算就行了
结果
1990/1991

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