若/ab-2/+(b-1)2=0,求1/ab+1/(a+1)(b+1)+1/(a+2)(b+2)+...1/(a+2010)(b+2010)的值

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若/ab-2/+(b-1)2=0,求1/ab+1/(a+1)(b+1)+1/(a+2)(b+2)+...1/(a+2010)(b+2010)的值

若/ab-2/+(b-1)2=0,求1/ab+1/(a+1)(b+1)+1/(a+2)(b+2)+...1/(a+2010)(b+2010)的值
若/ab-2/+(b-1)2=0,求1/ab+1/(a+1)(b+1)+1/(a+2)(b+2)+...1/(a+2010)(b+2010)的值

若/ab-2/+(b-1)2=0,求1/ab+1/(a+1)(b+1)+1/(a+2)(b+2)+...1/(a+2010)(b+2010)的值
|ab-2|+|b-1|=0
因为绝对值大于等于0,因此要等式成立,则:
ab-2=0
b-1=0
=>a=2,b=1
1/(ab)+1/(a+1)(b+1)+.+1/(a+2010)(b+2010)
=1/1*2+1/2*3+.+1/2011*2012
=1-1/2+1/2-1/3+.+1/2011-1/2012
=1-1/2012
=2011/2012