已知数列{an}满足a1=-1,an=[(3n+3)an+4n+6]/n,bn=3^(n-1)/an+2.求数列an的通向公式.设数列bn是的前n项和已知数列{an}满足a1=-1,an=[(3n+3)an+4n+6]/n,bn=3^(n-1)/an+2.(1)求数列an的通向公式.(2)设数列bn是的前n项和为sn,

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$已知数列{an}满足a1=-1,an=[(3n+3)an+4n+6]/n,bn=3^(n-1)/an+2.求数列an的通向公式.设数列bn是的前n项和已知数列{an}满足a1=-1,an=[(3n+3)an+4n+6]/n,bn=3^(n-1)/an+2.(1)求数列an的通向公式.(2)设数列bn是的前n项和为sn,$

已知数列{an}满足a1=-1,an=[(3n+3)an+4n+6]/n,bn=3^(n-1)/an+2.求数列an的通向公式.设数列bn是的前n项和已知数列{an}满足a1=-1,an=[(3n+3)an+4n+6]/n,bn=3^(n-1)/an+2.(1)求数列an的通向公式.(2)设数列bn是的前n项和为sn,
已知数列{an}满足a1=-1,an=[(3n+3)an+4n+6]/n,bn=3^(n-1)/an+2.求数列an的通向公式.设数列bn是的前n项和
已知数列{an}满足a1=-1,an=[(3n+3)an+4n+6]/n,bn=3^(n-1)/an+2.(1)求数列an的通向公式.(2)设数列bn是的前n项和为sn,求证n》2时,sn^2>2(s2/2+s3/3+...+sn/n

已知数列{an}满足a1=-1,an=[(3n+3)an+4n+6]/n,bn=3^(n-1)/an+2.求数列an的通向公式.设数列bn是的前n项和已知数列{an}满足a1=-1,an=[(3n+3)an+4n+6]/n,bn=3^(n-1)/an+2.(1)求数列an的通向公式.(2)设数列bn是的前n项和为sn,
已知数列{an}满足a1=-1,an=[(3n+3)an+4n+6]/n,bn=3^(n-1)/an+2.(1)求数列an的通向公式.(2)设数列bn是的前n项和为sn,求证n》2时,sn^2>2(s2/2+s3/3+...+sn/n

第一问移项合并同类项即可
第2问把an带进去求

5444

(1)an=3^n-1*n-2
(2)bn=1/n
Sn^2=(S(n-1)+1/n)^2=[S(n-1)]^2+2S(n-1)/n+1/n^2
=[S(n-1)]^2+[2S(n-1)+2/n]/n-1/n^2
=[S(n-1)]^2+2Sn/n-1/n^2
以此类推可得
Sn^2=S1^2-1/2^2-1/3^2-……-1/n^2+2(s2/2+...

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(1)an=3^n-1*n-2
(2)bn=1/n
Sn^2=(S(n-1)+1/n)^2=[S(n-1)]^2+2S(n-1)/n+1/n^2
=[S(n-1)]^2+[2S(n-1)+2/n]/n-1/n^2
=[S(n-1)]^2+2Sn/n-1/n^2
以此类推可得
Sn^2=S1^2-1/2^2-1/3^2-……-1/n^2+2(s2/2+s3/3+...sn/n)
只要证明n>=2时，
S1^2-1/2^2-1/3^2-……-1/n^2>=0即可
因为，S1=1
且对任意n>=1均有，1/n-1/(n+1)^2
=[(n+1)^2-n]/n(n+1)^2=(n^2+n+1)/n(n+1)^2>(n^2+n)/n(n+1)^2=1/(n+1)
故S1^2-1/2^2-1/3^2-……-1/n^2
=(1/1^2-1/2^2)-1/3^2-……-1/n^2
>1/2-1/3^2-……-1/n^2
>1/3-……-1/n^2
>1/(n-1)-1/n^2>0
原式得证。

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