2/(1*3)+｜1/2-1/4｜+2/(3*5)+｜1/4-1/6｜+2/(5*7)+｜1/6-1/8｜.2/(27*29)+｜1/28-1/30｜=?

来源：学生作业帮助网 编辑：作业帮 时间：2024/11/08 22:46:08

2/(1*3)+｜1/2-1/4｜+2/(3*5)+｜1/4-1/6｜+2/(5*7)+｜1/6-1/8｜.2/(27*29)+｜1/28-1/30｜=?
2/(1*3)+｜1/2-1/4｜+2/(3*5)+｜1/4-1/6｜+2/(5*7)+｜1/6-1/8｜.2/(27*29)+｜1/28-1/30｜=?

2/(1*3)+｜1/2-1/4｜+2/(3*5)+｜1/4-1/6｜+2/(5*7)+｜1/6-1/8｜.2/(27*29)+｜1/28-1/30｜=?
2/(1*3)+｜1/2-1/4｜+2/(3*5)+｜1/4-1/6｜+2/(5*7)+｜1/6-1/8｜.2/(27*29)+｜1/28-1/30｜
=（1-1/3+1/3-1/5+1/5-1/7+……+1/27-1/29）+（1/2-1/4+1/4-1/6+1/6-1/8+……+1/28-1/30）
=（1-1/29）+（1/2-1/30）
=28/29+7/15
=623/435

2/(3*5)=1/3-1/5
2/(5*7)=1/5-1/7
...以此类推
2/(1*3)+｜1/2-1/4｜+2/(3*5)+｜1/4-1/6｜+2/(5*7)+｜1/6-1/8｜......2/(27*29)+｜1/28-1/30｜
==（1-1/3+1/3-1/5+1/5-1/7+……+1/27-1/29）+（1/2-1/4+1/4-1/6+1/6-1/8+……+1/28-1/30）
=（1-1/29）+（1/2-1/30）
=28/29+7/15
=623/435

2/(1*3)+｜1/2-1/4｜+2/(3*5)+｜1/4-1/6｜+2/(5*7)+｜1/6-1/8｜......2/(27*29)+｜1/28-1/30｜
=1-1/3+1/2-1/4+1/3-1/5+1/4-1/6+1/5-1/7+1/6-1/8......1/27-1/29+1/28-1/30
=1+1/2-1/3+1/3-1/4+1/4-1/5+1/5-1/6+1/6......-1/29-1/30
=1+1/2-1/29-1/30
=(870+435-30-29)/870
=1246/870

本题=1+1/2-1/29-1/30= 623/435

(1-1/2^2)(1-1/3^2)(1-1/4^2).(1-1/2009^2), 1+2+3+4+1 1 2 3 4 1 2 3 4 1 2 3 4 1,2,3,4, 1 2 3 4 1 2 3 4 1,2,3,4, 1,2,3,4, 1,2,3,4, 1,2,3,4, 1 2 3 4 1,2,3,4, 1,2,3,4, 1,2,3,4, 1、2、3、4 1+2+3×4