thanksss!设数列{an}的前n项和为sn,已知a1=a,an+1=sn+3^n,n∈N* (1)设bn=sn-3^n,求数列{bn}(2)若an-1≥an,n∈N*,求a的取值范围
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![thanksss!设数列{an}的前n项和为sn,已知a1=a,an+1=sn+3^n,n∈N* (1)设bn=sn-3^n,求数列{bn}(2)若an-1≥an,n∈N*,求a的取值范围](/uploads/image/z/3806035-43-5.jpg?t=thanksss%21%E8%AE%BE%E6%95%B0%E5%88%97%7Ban%7D%E7%9A%84%E5%89%8Dn%E9%A1%B9%E5%92%8C%E4%B8%BAsn%2C%E5%B7%B2%E7%9F%A5a1%3Da%2Can%2B1%3Dsn%2B3%5En%2Cn%E2%88%88N%2A+%281%29%E8%AE%BEbn%3Dsn-3%5En%2C%E6%B1%82%E6%95%B0%E5%88%97%7Bbn%7D%EF%BC%882%EF%BC%89%E8%8B%A5an-1%E2%89%A5an%2Cn%E2%88%88N%2A%2C%E6%B1%82a%E7%9A%84%E5%8F%96%E5%80%BC%E8%8C%83%E5%9B%B4)
thanksss!设数列{an}的前n项和为sn,已知a1=a,an+1=sn+3^n,n∈N* (1)设bn=sn-3^n,求数列{bn}(2)若an-1≥an,n∈N*,求a的取值范围
thanksss!设数列{an}的前n项和为sn,已知a1=a,an+1=sn+3^n,n∈N* (1)设bn=sn-3^n,求数列{bn}
(2)若an-1≥an,n∈N*,求a的取值范围
thanksss!设数列{an}的前n项和为sn,已知a1=a,an+1=sn+3^n,n∈N* (1)设bn=sn-3^n,求数列{bn}(2)若an-1≥an,n∈N*,求a的取值范围
1:A(n+1)=S(n+1)-Sn
得:S(n+1)-Sn=Sn+3^n
∴S(n+1)=2Sn+3^n
∴S(n+1)-3*3^n=2Sn-2*3^n
∴S(n+1)-3^(n+1)=2(Sn-3^n)
∴B(n+1)=2Bn
又∵S1=A1=a,B1=a-3
∴Bn为以a-3为首项,2为公比的等比数列
∴Bn=(a-3)*2^(n-1)
2:a(n+1)=Sn+3^n=bn+2*3^n
a(n+1)-an
=bn+2*3^n-[b(n-1)+2*3^(n-1)]
=bn-b(n-1)+2[3^n-3^(n-1)]
=(a-3)*[2^(n-1)-2^(n-2)]+2[3^n-3^(n-1)]
=(a-3)*2^(n-2)+4*3^(n-1)>=0
a-3>=-4*3^(n-1)/2^(n-2)
=-12*(3/2)^(n-2)
a>=3-12*(3/2)^(n-2)
因为(3/2)^(n-2)最小=(3/2)^(1-2)=2/3
3-12*(3/2)^(n-2)最大=3-12*2/3=-5
a>=-5