二分之一乘三分之一等于二分之一减三分之一;三分之一乘四分之一等于三分之一减四分之一;

1个回答

  • 1/(1*2)+1/(2*3)+1/(3*4)+.+1/(99*100)=99/100

    1/(2*4)+1/(4*6)+1/(6*8)+.+1/(98*100)=49/200

    ------------------------------如果要过程:

    1/(1*2)+1/(2*3)+1/(3*4)+.+1/(99*100)

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

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

    =1-1/100

    =99/100

    1/(2*4)+1/(4*6)+1/(6*8)+.+1/(98*100)

    =[(4-2)/(2*4)+(6-4)/(4*6)+(8-6)/(6*8)+.+(100-98)/(98*100)]÷2

    =[(1/2-1/4)+(1/4-1/6)+(1/6-1/8)+.+(1/98-1/100)]÷2

    =[1/2-1/100]÷2

    =49/100÷2

    =49/200