1/3-1/15-1/35-1/63-1/99 等于多少?

来源：学生作业帮助网编辑：作业帮时间：2024/11/06 15:31:09

1/3-1/15-1/35-1/63-1/99 等于多少?
1/3-1/15-1/35-1/63-1/99 等于多少?

1/3-1/15-1/35-1/63-1/99 等于多少?
1/3-1/15-1/35-1/63-1/99
=1/(1*3)-1/(3*5)-1/(5*7)-1/(7*9)-1/(9*11)
=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(1-1/3-1/3+1/11)
=1/2(1/3+1/11)
=1/2*14/33
=7/33

=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)=5/11

1/3-1/15-1/35-1/63-1/99
=（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
=（1/3+1/11）*1/2
=14/33*1/2
=7/33

1/6+1/22

原是=2/3-1/(1*3)-1/(3*5)-1/(5*7)-1/(7*9)-1/(9*11)
=2/3-1/2[2/(1*3)+2/(3*5)+2/(5*7)+2/(7*9)+2/(9*11)]
=2/3-1/2[(1-1/3)+(1/3-1/5)+(1/5-1/7)+(1/7-1/9)+(1/9-1/11)]
=2/3-1/2[1-1/11]=2/3-5/11=22/33-15/33=7/33