已知|2b-2|与|b-1|互为相反数,试求'1/ab'+'1/'(a+1)(b+1)'+'1/(a+2)(b+)'+···'1/(a+2002)(b+2002)'的值
问题描述：
已知|2b-2|与|b-1|互为相反数,试求'1/ab'+'1/'(a+1)(b+1)'+'1/(a+2)(b+)'+···'1/(a+2002)(b+2002)'的值
答
应该是|ab-2|+|b-1|=0
所以ab-2=0,b-1=0
b=1
a=2/b=2
所以原式=1/1*2+1/2*3+……+1/2003*2004
=1-1/2+1/2-1/3+……+1/2003-1/2004
=1-1/2004
=2003/2004