已知数列{an}满足a1=1,an=a1+1/2a2+1/3a3+…+1/(n-1)a(n-1),若an=2006,则n=___

来源:学生作业帮助网 编辑:作业帮 时间:2024/04/29 11:24:20

已知数列{an}满足a1=1,an=a1+1/2a2+1/3a3+…+1/(n-1)a(n-1),若an=2006,则n=___
已知数列{an}满足a1=1,an=a1+1/2a2+1/3a3+…+1/(n-1)a(n-1),若an=2006,则n=___

已知数列{an}满足a1=1,an=a1+1/2a2+1/3a3+…+1/(n-1)a(n-1),若an=2006,则n=___
a2=a1=1
n>=3时
an+1=a1+1/2a2+.+1/n-1an-1+1/nan
两式相减得an+1-an=1/nan
即an+1=n+1/nan
即an+1/an=n+1/n
an+1/a2=(an+1/an)(an/an-1).(a3/a2)
=(n+1/n)(n/n-1).(3/2)
=n+1/2
即an+1=n+1/2
即an=n/2
an=2006,
n=4012