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

来源：学生作业帮编辑：神马作文网作业帮分类：数学作业时间：2024/11/13 01:41:18

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-1/y)+(1/(x+1)-1/(y+1))++……+(1/(x+1989)-1/(y+1989))
=(1/x-1/x+1)+(1/(x+1)-1/(x+2))++……+(1/(x+1989)-1/(x+1990))
=(1/x)-1/(x+1990)
代入x=1
=1-1/1991
=1990/1991

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