已知|a-1|+|b-2|=0,试求1/ab+1/(a+1)(b+1)+1/(a+2)(b+2)+.+1/(a+2009)(b+2009)的值

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已知|a-1|+|b-2|=0,试求1/ab+1/(a+1)(b+1)+1/(a+2)(b+2)+.+1/(a+2009)(b+2009)的值
已知|a-1|+|b-2|=0,试求1/ab+1/(a+1)(b+1)+1/(a+2)(b+2)+.+1/(a+2009)(b+2009)的值

已知|a-1|+|b-2|=0,试求1/ab+1/(a+1)(b+1)+1/(a+2)(b+2)+.+1/(a+2009)(b+2009)的值
|a-1|+|b-2|=0
绝对值大于等于0,相加为0则都等于0
所以a-1=0,b-2=0
a=1,b=2
所以1/ab+1/(a+1)(b+1)+1/(a+2)(b+2)+.+1/(a+2009)(b+2009)
=1/1*2+1/2*3+1/3*4+.+1/2010*2011
=1-1/2+1/2-1/3+1/3-1/4+.+1/2010-1/2011
=1-1/2011
=2010/2011