一乘二分之一减二乘三分之一减三乘四分之一
发布网友
发布时间：2024-10-22 09:11
共1个回答
热心网友
时间：2024-11-03 17:27
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
