已知√a-1+(ab-2)^2=0,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+(ab-2)^2=0,求1/ab+1/(a+1)(b+1)+1/(a+2)(b+2)+.+1/(a+2009)(b+2009)的值.
已知√a-1+(ab-2)^2=0,求1/ab+1/(a+1)(b+1)+1/(a+2)(b+2)+.+1/(a+2009)(b+2009)的值.

已知√a-1+(ab-2)^2=0,求1/ab+1/(a+1)(b+1)+1/(a+2)(b+2)+.+1/(a+2009)(b+2009)的值.
不知道对不对,
因为√a-1+(ab-2)^2=0,
所以√a-1=0,(ab-2)^2=0,
所以a-1=0,ab-2=0
所以a=1,b=2
则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