已知数列{an}满a1=1,an=a1+1/2a2+1/3a3+……+1/n-1an-1(n>=2,n属于N*)an=2006,n_数学解答

已知数列{an}满a1=1,an=a1+1/2a2+1/3a3+……+1/n-1an-1(n>=2,n属于N*)an=2006,n=
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人气：281 ℃　时间：2019-11-04 04:39:10

解答

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,
采纳我吧.谢谢哈~~
n=4012