若|ab-2|与(b-2)的平方互为相反数,试求代数式1/ab+1/(a+1)(b+1)+……1/(a+2012)(b+2012)

|ab-2|与(b-2)的平方互为相反数∴|ab-2|+(b-2)²=0∴ab-2=0b=2∴a=1b=21/ab+1/(a+1)(b+1)+……1/(a+2012)(b+2012) =1/1*2+1/2*3+1/3*4+……+1/2013*2014=1-1/2+1/2+1/3-1/3+1/4-1/4+……-1/2013+1/2013-1/2014=1...