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!

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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!
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!

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!
|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+1/3-1/4+.+1/2009-1/2010
=1-1/2010
=2009/2010