已知|ab-2|与|b-1|互为相反数,试求下列代数式的值1/ab+1/(a+1)(b+1)+1/(a+2)(b+2)+.+1/(a+2008)(b+2008)
问题描述：
已知|ab-2|与|b-1|互为相反数,试求下列代数式的值
1/ab+1/(a+1)(b+1)+1/(a+2)(b+2)+.+1/(a+2008)(b+2008)
答
|ab-2|与|b-1|互为相反数ab-2=0,b-1=0a=2,b=11/ab+1/(a+1)(b+1)+1/(a+2)(b+2)+.+1/(a+2008)(b+2008)=1/2*1+1/3*2+1/4*3+...+1/2010*2009=1-1/2+1/2-1/3+1/3-1/4+...+1/2009-1/2010=1-1/2010=2009/2010