(1):1/2!+2/3!+3/4!+····+(n-1)/n!(2):1*1!+2*2!+3*3!+·····+n*n!重谢!

来源:学生作业帮助网 编辑:作业帮 时间:2024/04/30 14:48:59
(1):1/2!+2/3!+3/4!+····+(n-1)/n!(2):1*1!+2*2!+3*3!+·····+n*n!重谢!

(1):1/2!+2/3!+3/4!+····+(n-1)/n!(2):1*1!+2*2!+3*3!+·····+n*n!重谢!
(1):1/2!+2/3!+3/4!+····+(n-1)/n!
(2):1*1!+2*2!+3*3!+·····+n*n!
重谢!

(1):1/2!+2/3!+3/4!+····+(n-1)/n!(2):1*1!+2*2!+3*3!+·····+n*n!重谢!
(注意下面带***的两行形式上的相似性)
(1)设结1/2!+2/3!+3/4!+····+(n-1)/n!=S
则S+1/n!=1/2!+2/3!+3/4!+·······+(n-1)/n!+1/n!***
=1/2!+2/3!+3/4!+····+(n-2)/(n-1)!+n/n!
=1/2!+2/3!+3/4!+····+(n-2)/(n-1)!+1/(n-1)!***
=.=1/2!+1/2!=1
所以S=1-1/n!
(2)设1*1!+2*2!+3*3!+·····+n*n!=S
则S-(n+1)!=1*1!+2*2!+3*3!+·····+n*n!-(n+1)!***
=1*1!+2*2!+3*3!+·····+n*n!-(n+1)n!
=1*1!+2*2!+3*3!+·····+(n-(n+1))n!
=1*1!+2*2!+3*3!+·····+(n-1)(n-1)!-n!***
=...=1*1!-2!=-1
所以S=(n+1)!-1

错位相消。。。20分也叫重谢???????
第一题。。你+1除2!+1除3!+。。。+1除n!就行了
第二题。。你+1!+2!+。。。+n!就行了

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