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=___

问题描述:

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=___
为什么a1=a2=1
先求通项公式

an=a1+(1/2)a2+(1/3)a3+…+[1/(n-2)]a(n-2)+[1/(n-1)]a(n-1),a(n-1)=a1+(1/2)a2+(1/3)a3+…+[1/(n-2)]a(n-2)an-a(n-1)=[1/(n-1)]a(n-1)an=[n/(n-1)]a(n-1)(1/n)an=[1/(n-1)]a(n-1)(1/n)an=[1/(n-1)]a(n-1)=……=(1/2...