已知正项数列{an}的前n项和为Sn,a1=2/3,且满足2S(n+1)+2Sn=3(an+1)^2(n属于N*)1,求数列{an}的通项公式an2,求证;当n>=2时,1/(a2)^2+1/(a3)^2+.+1/(an)^2
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![已知正项数列{an}的前n项和为Sn,a1=2/3,且满足2S(n+1)+2Sn=3(an+1)^2(n属于N*)1,求数列{an}的通项公式an2,求证;当n>=2时,1/(a2)^2+1/(a3)^2+.+1/(an)^2](/uploads/image/z/2131949-29-9.jpg?t=%E5%B7%B2%E7%9F%A5%E6%AD%A3%E9%A1%B9%E6%95%B0%E5%88%97%7Ban%7D%E7%9A%84%E5%89%8Dn%E9%A1%B9%E5%92%8C%E4%B8%BASn%2Ca1%3D2%2F3%2C%E4%B8%94%E6%BB%A1%E8%B6%B32S%28n%2B1%29%2B2Sn%3D3%28an%2B1%29%5E2%28n%E5%B1%9E%E4%BA%8EN%2A%291%2C%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%8Fan2%2C%E6%B1%82%E8%AF%81%EF%BC%9B%E5%BD%93n%3E%3D2%E6%97%B6%2C1%2F%28a2%29%5E2%2B1%2F%28a3%29%5E2%2B.%2B1%2F%28an%29%5E2)
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已知正项数列{an}的前n项和为Sn,a1=2/3,且满足2S(n+1)+2Sn=3(an+1)^2(n属于N*)1,求数列{an}的通项公式an2,求证;当n>=2时,1/(a2)^2+1/(a3)^2+.+1/(an)^2
已知正项数列{an}的前n项和为Sn,a1=2/3,且满足2S(n+1)+2Sn=3(an+1)^2(n属于N*)
1,求数列{an}的通项公式an
2,求证;当n>=2时,1/(a2)^2+1/(a3)^2+.+1/(an)^2
已知正项数列{an}的前n项和为Sn,a1=2/3,且满足2S(n+1)+2Sn=3(an+1)^2(n属于N*)1,求数列{an}的通项公式an2,求证;当n>=2时,1/(a2)^2+1/(a3)^2+.+1/(an)^2
(1)an=2n/3(递推一项,两式相减得an与an+1关系)
(2)即求n>=2时,∑1/n^2
a1=2/3,s1=a1=2/3,s2=a1+a2,
2(a1+a2)+2a1=3(a2)^2,a2=4/3
2(a1+a2+a3)+2(a1+a2)=3(a3)^2,a3=2
a4=8/3
....
an=2n/3
9/16 +9/36+9/64+...+9/(4n^2)=9(1/4+1/9+1/16+...+1/(n^2))/4<9*(π^2/6-1)/4<9/4
an=2n/3