若|ab-2|+|b-1|=0,试求1/ab +1/(a+1)(b+1) +1/(a+2)(b+2)+.+1/(a+2008)(b+2008)的值若|ab-2|+|b-1|=0,试求1/ab +1/(a+1)(b+1) +1/(a+2)(b+2)+.+1/(a+2008)(b+2008)的值
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![若|ab-2|+|b-1|=0,试求1/ab +1/(a+1)(b+1) +1/(a+2)(b+2)+.+1/(a+2008)(b+2008)的值若|ab-2|+|b-1|=0,试求1/ab +1/(a+1)(b+1) +1/(a+2)(b+2)+.+1/(a+2008)(b+2008)的值](/uploads/image/z/3795238-46-8.jpg?t=%E8%8B%A5%7Cab-2%7C%2B%7Cb-1%7C%3D0%2C%E8%AF%95%E6%B1%821%2Fab+%2B1%2F%28a%2B1%29%28b%2B1%29+%2B1%2F%28a%2B2%29%28b%2B2%29%2B.%2B1%2F%28a%2B2008%29%28b%2B2008%29%E7%9A%84%E5%80%BC%E8%8B%A5%7Cab-2%7C%2B%7Cb-1%7C%3D0%2C%E8%AF%95%E6%B1%821%2Fab+%2B1%2F%28a%2B1%29%28b%2B1%29+%2B1%2F%28a%2B2%29%28b%2B2%29%2B.%2B1%2F%28a%2B2008%29%28b%2B2008%29%E7%9A%84%E5%80%BC)
若|ab-2|+|b-1|=0,试求1/ab +1/(a+1)(b+1) +1/(a+2)(b+2)+.+1/(a+2008)(b+2008)的值若|ab-2|+|b-1|=0,试求1/ab +1/(a+1)(b+1) +1/(a+2)(b+2)+.+1/(a+2008)(b+2008)的值
若|ab-2|+|b-1|=0,试求1/ab +1/(a+1)(b+1) +1/(a+2)(b+2)+.+1/(a+2008)(b+2008)的值
若|ab-2|+|b-1|=0,试求1/ab +1/(a+1)(b+1) +1/(a+2)(b+2)+.+1/(a+2008)(b+2008)的值
若|ab-2|+|b-1|=0,试求1/ab +1/(a+1)(b+1) +1/(a+2)(b+2)+.+1/(a+2008)(b+2008)的值若|ab-2|+|b-1|=0,试求1/ab +1/(a+1)(b+1) +1/(a+2)(b+2)+.+1/(a+2008)(b+2008)的值
|ab-2|+|b-1|=0,
所以ab-2=0 b-1=0
a=2 b=1
1/ab +1/(a+1)(b+1) +1/(a+2)(b+2)+.+1/(a+2008)(b+2008)
=1/(1×2)+1/(2×3)+……+1/(2009×2010)
=1-1/2+1/2-1/3+……+1/2009-1/2010
=1-1/2010
=2009/2010
由|ab-2|+|b-1|=0可知b=1,a=2
1/ab +1/(a+1)(b+1) +1/(a+2)(b+2)+......+1/(a+2008)(b+2008)=1/(1X2)+1/(2X3)+...+1/(2009X2010)=(1-1/2)+(1/2-1/3)+(1/3-1/4)+....+(1/2009-1/2010)=1-1/2010=2009/2010