a(n+1)=2an-a(n-1) 3bn-b(n-1)=n数列{an},a(n+1)=2an-a(n-1),a1=1/4,a2=3/4.数列{bn},3bn-b(n-1)=n,{bn}前n项和Sn1.求证数列{bn-an}是等比2.若当且仅当n=4时,Sn取得最小值,求b1取值范围
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![a(n+1)=2an-a(n-1) 3bn-b(n-1)=n数列{an},a(n+1)=2an-a(n-1),a1=1/4,a2=3/4.数列{bn},3bn-b(n-1)=n,{bn}前n项和Sn1.求证数列{bn-an}是等比2.若当且仅当n=4时,Sn取得最小值,求b1取值范围](/uploads/image/z/634735-55-5.jpg?t=a%28n%2B1%29%3D2an-a%28n-1%29+3bn-b%28n-1%29%3Dn%E6%95%B0%E5%88%97%7Ban%7D%2Ca%28n%2B1%29%3D2an-a%28n-1%29%2Ca1%3D1%2F4%2Ca2%3D3%2F4.%E6%95%B0%E5%88%97%7Bbn%7D%2C3bn-b%28n-1%29%3Dn%2C%7Bbn%7D%E5%89%8Dn%E9%A1%B9%E5%92%8CSn1.%E6%B1%82%E8%AF%81%E6%95%B0%E5%88%97%7Bbn-an%7D%E6%98%AF%E7%AD%89%E6%AF%942.%E8%8B%A5%E5%BD%93%E4%B8%94%E4%BB%85%E5%BD%93n%3D4%E6%97%B6%2CSn%E5%8F%96%E5%BE%97%E6%9C%80%E5%B0%8F%E5%80%BC%2C%E6%B1%82b1%E5%8F%96%E5%80%BC%E8%8C%83%E5%9B%B4)
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a(n+1)=2an-a(n-1) 3bn-b(n-1)=n数列{an},a(n+1)=2an-a(n-1),a1=1/4,a2=3/4.数列{bn},3bn-b(n-1)=n,{bn}前n项和Sn1.求证数列{bn-an}是等比2.若当且仅当n=4时,Sn取得最小值,求b1取值范围
a(n+1)=2an-a(n-1) 3bn-b(n-1)=n
数列{an},a(n+1)=2an-a(n-1),a1=1/4,a2=3/4.数列{bn},3bn-b(n-1)=n,{bn}前n项和Sn
1.求证数列{bn-an}是等比
2.若当且仅当n=4时,Sn取得最小值,求b1取值范围
a(n+1)=2an-a(n-1) 3bn-b(n-1)=n数列{an},a(n+1)=2an-a(n-1),a1=1/4,a2=3/4.数列{bn},3bn-b(n-1)=n,{bn}前n项和Sn1.求证数列{bn-an}是等比2.若当且仅当n=4时,Sn取得最小值,求b1取值范围
1.
a(n+1)=2an-a(n-1)
a(n+1)-an=an-a(n-1)
an为以1/4为首项,1/2为公差的等差数列
an=n/2-1/4
bn-an=bn-n/2+1/4
b(n+1)-a(n+1)=bn/3+n/3+1/3-n/2-1/2+1/4=bn/3-n/6+1/12=(bn-an)/3
得证
2.
b4=(b1+49)/270
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