已知数列﹛an﹜的前n项和为Sn,a1=1,且2nSn+1-2(n+1)Sn=n²+n(n∈N*).(1)求数列{an}的通项公式;(2)设bn=n/2(n+3)Sn,求数列{bn}的前n项和Tn;(3)证明:n≥2时,1/(a2的三次方)+1/(a3的三次方)+1/(
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![已知数列﹛an﹜的前n项和为Sn,a1=1,且2nSn+1-2(n+1)Sn=n²+n(n∈N*).(1)求数列{an}的通项公式;(2)设bn=n/2(n+3)Sn,求数列{bn}的前n项和Tn;(3)证明:n≥2时,1/(a2的三次方)+1/(a3的三次方)+1/(](/uploads/image/z/1132173-45-3.jpg?t=%E5%B7%B2%E7%9F%A5%E6%95%B0%E5%88%97%EF%B9%9Ban%EF%B9%9C%E7%9A%84%E5%89%8Dn%E9%A1%B9%E5%92%8C%E4%B8%BASn%2Ca1%3D1%2C%E4%B8%942nSn%2B1%EF%BC%8D2%28n%2B1%29Sn%3Dn%26%23178%3B%2Bn%28n%E2%88%88N%2A%29.%EF%BC%881%EF%BC%89%E6%B1%82%E6%95%B0%E5%88%97%7Ban%7D%E7%9A%84%E9%80%9A%E9%A1%B9%E5%85%AC%E5%BC%8F%EF%BC%9B%EF%BC%882%EF%BC%89%E8%AE%BEbn%3Dn%2F2%28n%2B3%29Sn%2C%E6%B1%82%E6%95%B0%E5%88%97%7Bbn%7D%E7%9A%84%E5%89%8Dn%E9%A1%B9%E5%92%8CTn%EF%BC%9B%EF%BC%883%EF%BC%89%E8%AF%81%E6%98%8E%EF%BC%9An%E2%89%A52%E6%97%B6%2C1%2F%EF%BC%88a2%E7%9A%84%E4%B8%89%E6%AC%A1%E6%96%B9%EF%BC%89%2B1%2F%EF%BC%88a3%E7%9A%84%E4%B8%89%E6%AC%A1%E6%96%B9%EF%BC%89%2B1%2F%28)
已知数列﹛an﹜的前n项和为Sn,a1=1,且2nSn+1-2(n+1)Sn=n²+n(n∈N*).(1)求数列{an}的通项公式;(2)设bn=n/2(n+3)Sn,求数列{bn}的前n项和Tn;(3)证明:n≥2时,1/(a2的三次方)+1/(a3的三次方)+1/(
已知数列﹛an﹜的前n项和为Sn,a1=1,且2nSn+1-2(n+1)Sn=n²+n(n∈N*).(1)求数列{an}的通项公式;(2)设bn=n/2(n+3)Sn,求数列{bn}的前n项和Tn;(3)证明:n≥2时,1/(a2的三次方)+1/(a3的三次方)+1/(a4的三次方)+……+1/(an的三次方)<1/4
已知数列﹛an﹜的前n项和为Sn,a1=1,且2nSn+1-2(n+1)Sn=n²+n(n∈N*).(1)求数列{an}的通项公式;(2)设bn=n/2(n+3)Sn,求数列{bn}的前n项和Tn;(3)证明:n≥2时,1/(a2的三次方)+1/(a3的三次方)+1/(
2nSn+1-2(n+1)Sn=n²+n
两边同时处以2n(n+1)
∴ S(n+1)/(n+1) - Sn/n=1/2
∴ {Sn/n}是等差数列,首项为a1/1=1, 公差是1/2
∴ Sn/n=1+(1/2)(n-1)=(n+1)/2
∴ Sn=n(n+1)/2
(1) n=1, a1=1
(2) n≥2
an=S...
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2nSn+1-2(n+1)Sn=n²+n
两边同时处以2n(n+1)
∴ S(n+1)/(n+1) - Sn/n=1/2
∴ {Sn/n}是等差数列,首项为a1/1=1, 公差是1/2
∴ Sn/n=1+(1/2)(n-1)=(n+1)/2
∴ Sn=n(n+1)/2
(1) n=1, a1=1
(2) n≥2
an=Sn-S(n-1)
=n(n+1)/2-n(n-1)/2
=n*[(n+1)-(n-1)]/2
=n
n=1也满足上式
∴ an=n
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