(a-1)的平方根+(ab-2)的平方=0
a-1=0,ab-2=0
a=1,b=2
所以
1/ab+1/(a+1)(b+1)+1/(a+2)(b+2)+...+1/(a+2010)(b+2010)
=1/1×2+1/2×3+1/3×4+.+1/2011×2012
=1-1/2+1/2-1/3+1/3-1/4+.+1/2011-1/2012
=1-1/2012
=2011/2012