2×5分之一+3×5分之一+8×11分之一+...+20×23分之一 简便

• .1.参考答案-1
  1/(2*5)=1/10=1/3*(1/2-1/5),
  1/(5*8)=1/40=1/3*(1/5-1/8),
  1/(8*11)=1/88=1/3*(1/8-1/11),
  .
  1/(20*23)=.=1/3*(1/20-1/23),
  ∴原式=1/3*(1/2-1/5+1/5-1/8+1/8-1/11+...+1/20-1/23)
  =1/3*(1/2-1/23)
  =(1/3)*(21/46)
  =7/46