Question

已知|ab-2|与（b-1）的平方互为相反数,试求代数式：

Answer 1

|ab-2|+(b-1)²=0

∴ab-2=0,b-1=0

∴a=2,b=1

∴原式=1/(1×2)+1/(2×3)+1/(3×4)+…+1/(2014×2015)

=(1-1/2)+(1/2-1/3)+(1/3-1/4)+…+(1/2014-1/2015)

=1-1/2+1/2-1/3+1/3-1/4+…+1/2014-1/2015

=1-1/2015

=2014/2015