(ab-2)*(ab-2)+|b-1|=0,
ab-2=0,b-1=0
b=1,a=2.
1/(a+1)(b+1)+1/(a+2)(b+2)+~+1/(a+2011)(b+2011)
=1/2*3+1/3*4+.+1/2012*2013
=1/2-1/3+1/3-1/4+.+1/2012-2013
=1/2-1/2013
=2011/4026