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已知Ix-2I+Iy-4I=0求1/xy+1/(x+2)(y+2)+1/(x+4)(y+4)+.+1/(x+2010)+

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已知Ix-2I+Iy-4I=0求1/xy+1/(x+2)(y+2)+1/(x+4)(y+4)+.+1/(x+2010)+Y+2010)
已知Ix-2I+Iy-4I=0求1/xy+1/(x+2)(y+2)+1/(x+4)(y+4)+.+1/(x+2010)+
∵Ix-2I+Iy-4I=0,∴x=2,y=4 ; ∴1/xy+1/(x+2)(y+2)+1/(x+4)(y+4)+.+1/(x+2010)+Y+2010) =1/2*4+1/4*6+1/6*8+……+1/2012*2014 =(1/2-1/4)/2+(1/4-1/6)/2+(1/6-1/8)/2+……+(1/2012-1/2014)/2 =(1/2-1/4+1/4-1/6+1/6-1/8+……+1/2012-1/2014)/2 =(1/2-1/2014)/2 =503/2014 有疑问欢迎追问,