已知|a-b-1|与|b-1|互为相反数;试求ab/1+(a+1)(b+1)/1+(a+2)(b+2)/1+…+(a+2008)(b+2008)的值 有点儿急!
问题描述：
已知|a-b-1|与|b-1|互为相反数;试求ab/1+(a+1)(b+1)/1+(a+2)(b+2)/1+…+(a+2008)(b+2008)的值 有点儿急!
答
|a-b-1|与|b-1|互为相反数∴ |a-b-1|＋|b-1|＝0∵ 绝对值非负.∴ a-b-1=0,b-1=0∴ b=1,a=2∴ ab/1+(a+1)(b+1)/1+(a+2)(b+2)/1+…+(a+2008)(b+2008)=1/(1*2)+1/(2*3)+1/(3*4)+.+1/(2009*2010)=1/1-1/2+1/2-1/3+1/3...