1/6+1/12+1/20+1/30+1/42

1个回答

  • 1/2+1/6+1/12+1/20+1/30+1/42

    =(1-1/2)+(1/2-1/3)+(1/3-1/4)+(1/4-1/5)+(1/5-1/6)+(1/6-1/7)

    =1-1/2+1/2-1/3+1/3-1/4+1/4-1/5+1/5-1/6+1/6-1/7

    =1-(1/2-1/2)-(1/3-1/3)-(1/4-1/4)-(1/5-1/5)-(1/6-1/6)-1/7

    =1-0-0-0-0-0-1/7

    =6/7