1-1/5-1/45-1/117-1/221-1/375
来源：学生作业帮助网 编辑：六六作业网 时间：2024/12/26 04:49:08
1-1/5-1/45-1/117-1/221-1/375
1-1/5-1/45-1/117-1/221-1/375
1-1/5-1/45-1/117-1/221-1/375
1-1/5-1/45-1/117-1/221-1/357
=1-1/(1x5)-1/(5x9)-1/(9x13)-1/(13x17)-1/(17x21)
=1-[1/(1x5)+1/(5x9)+1/(9x13)+1/(13x17)+1/(17x21)]
=1-[1/4(1-1/5)+1/4(1/5-1/9)+1/4(1/9-1/13)+1/4(1/13-1/17)+1/4(1/17-1/21)]
=1-1/4(1-1/5+1/5-1/9+1/9-1/13+1/13-1/17+1/17-1/21)
=1-1/4(1-1/21)
=1-1/4x20/21
=1-5/21
=16/21
你题目的375应该是打错了，如果是357还能做
1-1/5-1/45-1/117-1/221-1/357
=1-1/5-1/5*1/9-1/9*1/13-1/13*1/17-1/17*1/21
=1/4x(1-1/5)+1/4x(1/5-1/9)+1/4x(1/9-1/13)+1/4x(1/13-1/17)+1/4x(1/17-1/21)
=1/4x(1-1/5+1/5-1/9+1/9-1/13+1/13-1/17+1/17-1/21)
=1/4x(1-1/21)
=5/21
4858/6375
=1-1/5-1/(5*9)-1/(9*13)-1/(13*17)-1/(17*21)
=1-1/4(1-1/5+1/5-1/9+1/9-1/13*1/13-1/17+1/17-1/21)
=1-1/4* (1-1/21)
=1-1/4 *20/21
=1-5/21
=16/21
原式=1-1/5-1/5*9-1/9*13-1/13*17-1/17*21
=1-(1/5+1/5*9+1/9*13+1/13*17+1/17*21)
=1-(4/5+1/5-1/9+1/9-1/13+1/13-/17+1/17-1/21)/4
=1-(1-1/21)/4
...
全部展开
原式=1-1/5-1/5*9-1/9*13-1/13*17-1/17*21
=1-(1/5+1/5*9+1/9*13+1/13*17+1/17*21)
=1-(4/5+1/5-1/9+1/9-1/13+1/13-/17+1/17-1/21)/4
=1-(1-1/21)/4
=1-(20/21)/4
=16/21
楼主原式最后的1/375应该是1/357。
【俊狼猎英】团队为您解答。祝你进步。请采纳。
收起