数列{an}的通项公式满足a1=1,an+1=n/n+1xan,求an.急用!

来源:学生作业帮助网 编辑:六六作业网 时间:2024/11/24 11:25:44
数列{an}的通项公式满足a1=1,an+1=n/n+1xan,求an.急用!数列{an}的通项公式满足a1=1,an+1=n/n+1xan,求an.急用!数列{an}的通项公式满足a1=1,an+1

数列{an}的通项公式满足a1=1,an+1=n/n+1xan,求an.急用!
数列{an}的通项公式满足a1=1,an+1=n/n+1xan,求an.急用!

数列{an}的通项公式满足a1=1,an+1=n/n+1xan,求an.急用!
由an+1=n/n+1xan可得an+1/an=n/n+1
所以a2/a1=1/2
a3/a2=2/3
……
an/an-1=(n-1)/n
以上各式相乘得an/a1=1/n
故an=1/n

a2/a1=1/2;
a3/a2=2/3;
……;
an/a(n-1)=(n-1)/n;
连乘,得an/a1=1/n;
an=a1/n=1/n

因为an+1/an=n+1/n
所以an/an-1=n/n-1
an=an/(an-1)×an-1/an-2…a2/a1*a1=n