已知x^2+y^2-2x-4y+5=0,求1/xy+1/(x+1)(y+1)+1/(x+2)(y+2)+……1/（x+2

来源：学生作业帮编辑：作业帮分类：数学作业时间：2024/05/15 16:23:58

已知x^2+y^2-2x-4y+5=0,求1/xy+1/(x+1)(y+1)+1/(x+2)(y+2)+……1/（x+2009）（y+2009)

x^2+y^2-2x-4y+5=0
则(x-1)^2+(y-2)^2=0
x=1,y=2
原式＝1/(1*2)+1/(2*3)+.+1/(n*(n+1))+.+1/(2010*2011)
＝1/1-1/2+1/2-1/3+.+1/n-1/(n+1)+.+1/2009-1/2010+1/2010-1/2011
＝1-1/2011＝2010/2011

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