1/1*3+1/3*5+...1/49*51的答案

来源：百度知道 编辑：UC知道 时间：2024/09/22 07:29:50
1/1*3+1/3*5+...1/49*51 过程

1/1*3+1/3*5+...1/49*51
=1/2 * [（1-1/3）+(1/3-1/5)+(1/5-1/7)…………]前后消去很多
=1/2 * (1-1/51)
=25/51

25/51

因为1/（1*3）=(1/1-1/3)/2,1/(3*5）=(1/3-1/5)/2,1(5*7)=(1/5-1/7)/2...1(49*51)=(1/49-1/51)/2
所以1/（1*3）+1/（3*5）+1/（5*7）+…+1/（49*51）=(1-1/3+1/3-1/5+1/5...+1/49-1/51)
=(1-1/51)/2=25/51

1-1/51
等于 50/51

1/1*3可分为 1/1-1/3 1/3*5 = 1/3-1/5

依次类推 该式只余 1-1/51

它的规律
1/(2n-1)(2n+1)=[1/(2n-1)-1/(2n+1)]/2

1/1*3+1/3*5+...1/49*51=(1-1/3+1/3-1/5+1/5-1/7+……+1/49-1/51)/2=(1-1/51)/2=25/51

1/1*3+1/3*5+...1/49*51=
(1/2)*[(1-1/3)+(1/3-1/5)(1/5-1/7)+..........+(1/49-1/51 )]=
(1/2)*[(1-1/51)=
(1/2)*(50/51)=
25/51

原式=(1-1/3)*1/2+(1/3-1/5)*1/2+(1/5-1/7)*1/2+……(1/49-1/51)*1/2
=(1-1/3+1/3-1/5+1/5-1/7+1/7……1/49-1/51)*1/2
=(1-1/51)*1/2
= 50/51*1/2
= 25/51