已知|x-2|+(y-4)²=0,求1/xy+1/(x+2)(y+2)+1/(x+4)(y+4)+.+1/(x
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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
|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
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