Question

我们知道一乘二分之一=一减二分之一二乘三分之一=二分之一减三分之一三乘四分之一=三分之一减四分之一,将以上三个等式两边分

Answer 1

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