由已知得a=1,b=2,所以1/(a+k)(b+k)=1/(k+1)(k+2)=1/(k+1)-1/(k+2),所以原式值为2001/2002
若a^2+b^2-2a-4b+5=0,求1/ab+1/(a+1)(b+1)+...+1/(a+2000)(a+2000)
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