已知(a-1)^2+|ab-2|=0,求1/ab+1/(a+1)(b+1)+1/(a+2)(b+2)+…+1/(a+1998)(b+1998)

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已知(a-1)^2+|ab-2|=0,求1/ab+1/(a+1)(b+1)+1/(a+2)(b+2)+…+1/(a+1998)(b+1998)
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已知(a-1)^2+|ab-2|=0,求1/ab+1/(a+1)(b+1)+1/(a+2)(b+2)+…+1/(a+1998)(b+1998)
已知(a-1)^2+|ab-2|=0,求1/ab+1/(a+1)(b+1)+1/(a+2)(b+2)+…+1/(a+1998)(b+1998)

已知(a-1)^2+|ab-2|=0,求1/ab+1/(a+1)(b+1)+1/(a+2)(b+2)+…+1/(a+1998)(b+1998)
由题可知a=1,b=2
1/ab+1/(a+1)(b+1)+1/(a+2)(b+2)+…+1/(a+1998)(b+1998)
=1/1*2+1/2*3+1/3*4+…+1/1999*2000
=1-1/2+1/2-1/3+1/3-1/4…+1/1999-1/2000
=1-1/2000
=1999/2000