若｜ab-2｜+｜b-1｜=0,试求1/ab+1/(a+b)(b+1)+…+1/(a+2012)(b+2012)
问题描述：
若｜ab-2｜+｜b-1｜=0,试求1/ab+1/(a+b)(b+1)+…+1/(a+2012)(b+2012)
答
若｜ab-2｜+｜b-1｜=0
b-1=0 b=1
ab-2=0 a=2
1/ab+1/(a+b)(b+1)+…+1/(a+2012)(b+2012)
=1/1x2+1/2x3+……+1/2003x2004
=1-1/2+1/2-1/3+……+1/2003-1/2004
=1-1/2004
=2003/2004