已知数列{an},an>0且3*a(n+1)²=an*(an-2*a(n+1)),a1=1求证 an是等比和其通项公式若bn=1/n()log3a1+loga2+...+log3an),且数列{bn}的前n项和为Tn求Tnmax
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![已知数列{an},an>0且3*a(n+1)²=an*(an-2*a(n+1)),a1=1求证 an是等比和其通项公式若bn=1/n()log3a1+loga2+...+log3an),且数列{bn}的前n项和为Tn求Tnmax](/uploads/image/z/1159250-50-0.jpg?t=%E5%B7%B2%E7%9F%A5%E6%95%B0%E5%88%97%7Ban%7D%2Can%3E0%E4%B8%943%2Aa%28n%2B1%29%26sup2%3B%3Dan%2A%28an-2%2Aa%28n%2B1%29%29%2Ca1%3D1%E6%B1%82%E8%AF%81+an%E6%98%AF%E7%AD%89%E6%AF%94%E5%92%8C%E5%85%B6%E9%80%9A%E9%A1%B9%E5%85%AC%E5%BC%8F%E8%8B%A5bn%3D1%2Fn%28%29log3a1%2Bloga2%2B...%2Blog3an%29%2C%E4%B8%94%E6%95%B0%E5%88%97%7Bbn%7D%E7%9A%84%E5%89%8Dn%E9%A1%B9%E5%92%8C%E4%B8%BATn%E6%B1%82Tnmax)
已知数列{an},an>0且3*a(n+1)²=an*(an-2*a(n+1)),a1=1求证 an是等比和其通项公式若bn=1/n()log3a1+loga2+...+log3an),且数列{bn}的前n项和为Tn求Tnmax
已知数列{an},an>0且3*a(n+1)²=an*(an-2*a(n+1)),a1=1
求证 an是等比和其通项公式
若bn=1/n()log3a1+loga2+...+log3an),且数列{bn}的前n项和为Tn求Tnmax
已知数列{an},an>0且3*a(n+1)²=an*(an-2*a(n+1)),a1=1求证 an是等比和其通项公式若bn=1/n()log3a1+loga2+...+log3an),且数列{bn}的前n项和为Tn求Tnmax
(1)3*a(n+1)2=an*(an-2*a(n+1))
(3a(n+1)-an)(a(n+1)+an)=0
an>0,3a(n+1)=an,所以an是等比数列,且an=(1/3)^(n-1)
(2)log3an=1-n
bn=1/n(log3a1+loga2+...+log3an)=1/n(0-1-2-...+1-n)=(1-n)/2
Tn=n/2-(1/2+2/2+3/2+...+n/2)=(n-n^2)/4
(Tn)max=T1=0