计算11×2+12×3+13×4+…+198×99+199×100．

Question

计算(1)/(1×2)+(1)/(2×3)+(1)/(3×4)+…+(1)/(98×99)+(1)/(99×100)．

Answer 1

原式=（(1)/(1)-(1)/(2)）+（(1)/(2)-(1)/(3)）+（(1)/(3)-(1)/(4)）+（(1)/(98)-(1)/(99)）+（(1)/(99)-(1)/(100)）
=(1)/(1)-(1)/(2)+(1)/(2)-(1)/(3)+(1)/(3)-(1)/(4)+(1)/(98)-(1)/(99)+(1)/(99)-(1)/(100)
=1-(1)/(100)
=(99)/(100)．