若|x-1|+|y-2|=0,求1/xy+1/(x+1)(y+1)+1/(x+2)(y+2)+.+1/(x+2009)(

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若|x-1|+|y-2|=0,求1/xy+1/(x+1)(y+1)+1/(x+2)(y+2)+.+1/(x+2009)(y+2009)的值
十分钟内的答案,经过认可,

|x-1|+|y-2|=0
x=1,y=2
1/xy+1/(x+1)(y+1)+1/(x+2)(y+2)+.+1/(x+2009)(y+2009)
=1/2+1/6+1/12+.+1/(2010*2011)
=1-1/2+1/2-1/3+.+1/2010-1/2011
=1-1/2011
=2010/2011

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