1/1x3+1/3x5+1/5x7+1/7x9+1/9x11=?

来源：学生作业帮助网编辑：作业帮时间：2024/04/29 20:08:27

1/1x3+1/3x5+1/5x7+1/7x9+1/9x11=?
1/1x3+1/3x5+1/5x7+1/7x9+1/9x11=?

1/1x3+1/3x5+1/5x7+1/7x9+1/9x11=?
=(1/2)×(1-1/3)+(1/2)×(1/3-1/5)+(1/2)×(1/5-1/7)+(1/2)×(1/7-1/9)+(1/2)×(1/9-1/11)
=(1/2)×(1-1/3+1/3-1/5+1/5-1/7+1/7-1/9+1/9-1/11)
=(1/2)×(1-1/11)
=5/11

1/1x3+1/3x5+1/5x7+1/7x9+1/9x11
=1/2*(1-1/3+1/3-1/5+1/5-1/7+1/7-1/9+1/9-1/11)
=1/2*(1-1/11)
=1/2*10/11
=5/11

1/2（1-1/3-1/3-1/5+1/5-1/7+1/7-1/9+1/9-1/11）
=1/2*10/11=5/11