1/5*9+1/9*13+1/13*17+...+1/101*105

来源：百度知道 编辑：UC知道 时间：2024/06/05 14:07:58
每项的分子是1，分母是差是4的两个数，次项的小数是前项的大数

等于1/21

1/5*9 = (1/5-1/9)/4
1/9*13 =(1/9-1/13)/4
1/13*17=(1/13-1/17)/4
依次类推
原试等于
(1/5-1/9+1/9-1/13+1/13-1/17+1/17-...-1/101+1/101-1/105)/4
=(1/5-1/105)/4=1/21

=1/4*(1/5-1/9+1/9-1/13+……+1/101-1/105)
=1/4*(1/5-1/105)
=1/4*20/105
=1/21

1/5*9+1/9*13+1/13*17+...+1/101*105
=1/4*[(1/5-1/9)+(1/9-1/13)+(1/13-1/17)+....+(1/101-1/05)]
=1/4*[1/5-1/105]
=1/4*20/105
=1/4*4/21
=1/21