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)(_数学解答

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!

人气：347 ℃　时间：2020-07-07 04:22:12

解答

|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...