已知|x-2|+(y-4)²=0,求1/xy+1/(x+2)(y+2)+1/(x+4)(y+4)+.+1/(x+2012)(y+2012)的值
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![已知|x-2|+(y-4)²=0,求1/xy+1/(x+2)(y+2)+1/(x+4)(y+4)+.+1/(x+2012)(y+2012)的值](/uploads/image/z/4043821-13-1.jpg?t=%E5%B7%B2%E7%9F%A5%7Cx-2%7C%2B%EF%BC%88y-4%EF%BC%89%26%23178%3B%3D0%2C%E6%B1%821%2Fxy%2B1%2F%EF%BC%88x%2B2%EF%BC%89%EF%BC%88y%2B2%EF%BC%89%2B1%2F%EF%BC%88x%2B4%EF%BC%89%EF%BC%88y%2B4%EF%BC%89%2B.%2B1%2F%EF%BC%88x%2B2012%EF%BC%89%EF%BC%88y%2B2012%EF%BC%89%E7%9A%84%E5%80%BC)
已知|x-2|+(y-4)²=0,求1/xy+1/(x+2)(y+2)+1/(x+4)(y+4)+.+1/(x+2012)(y+2012)的值
已知|x-2|+(y-4)²=0,求1/xy+1/(x+2)(y+2)+1/(x+4)(y+4)+.+1/(x+2012)(y+2012)的值
已知|x-2|+(y-4)²=0,求1/xy+1/(x+2)(y+2)+1/(x+4)(y+4)+.+1/(x+2012)(y+2012)的值
|x-2|+(y-4)²=0
x-2=y-4=0
所以x=2,y=4
原式=1/2*4+1/4*6+……+1/2014*2016
=1/2*(1/2-1/4+1/4-1/6+……+1/2014-1/206)
=1/2*(1/2-1/2006)
=501/2006
x-2=y-4=0
所以x=2,y=4
原式=1/2*4+1/4*6+……+1/2014*2016
=1/2*(1/2-1/4+1/4-1/6+……+1/2014-1/206)
=1/2*(1/2-1/2006)
=501/2006