设数列{an}的前n项和为Sn,且满足S1=2,S(n+1)=3Sn+2(n=1,2,3) 设bn=2,S(n+1)=3Sn+2(n=1,2,3.) 注:n+1设数列{an}的前n项和为Sn,且满足S1=2,Sn+1=3Sn+2(n=1,2,3) 设bn=2,Sn+1=3Sn+2(n=1,2,3.)设bn=an比Sn平方,求证b1+b2+b3.bn
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![设数列{an}的前n项和为Sn,且满足S1=2,S(n+1)=3Sn+2(n=1,2,3) 设bn=2,S(n+1)=3Sn+2(n=1,2,3.) 注:n+1设数列{an}的前n项和为Sn,且满足S1=2,Sn+1=3Sn+2(n=1,2,3) 设bn=2,Sn+1=3Sn+2(n=1,2,3.)设bn=an比Sn平方,求证b1+b2+b3.bn](/uploads/image/z/3621922-34-2.jpg?t=%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%E4%B8%94%E6%BB%A1%E8%B6%B3S1%3D2%2CS%28n%2B1%29%3D3Sn%2B2%28n%3D1%2C2%2C3%29+%E8%AE%BEbn%3D2%2CS%28n%2B1%29%3D3Sn%2B2%28n%3D1%2C2%2C3.%29+%E6%B3%A8%EF%BC%9An%2B1%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%E4%B8%94%E6%BB%A1%E8%B6%B3S1%3D2%2CSn%2B1%3D3Sn%2B2%28n%3D1%2C2%2C3%29+%E8%AE%BEbn%3D2%2CSn%2B1%3D3Sn%2B2%28n%3D1%2C2%2C3.%29%E8%AE%BEbn%3Dan%E6%AF%94Sn%E5%B9%B3%E6%96%B9%2C%E6%B1%82%E8%AF%81b1%2Bb2%2Bb3.bn)
设数列{an}的前n项和为Sn,且满足S1=2,S(n+1)=3Sn+2(n=1,2,3) 设bn=2,S(n+1)=3Sn+2(n=1,2,3.) 注:n+1设数列{an}的前n项和为Sn,且满足S1=2,Sn+1=3Sn+2(n=1,2,3) 设bn=2,Sn+1=3Sn+2(n=1,2,3.)设bn=an比Sn平方,求证b1+b2+b3.bn
设数列{an}的前n项和为Sn,且满足S1=2,S(n+1)=3Sn+2(n=1,2,3) 设bn=2,S(n+1)=3Sn+2(n=1,2,3.) 注:n+1
设数列{an}的前n项和为Sn,且满足S1=2,Sn+1=3Sn+2(n=1,2,3)
设bn=2,Sn+1=3Sn+2(n=1,2,3.)
设bn=an比Sn平方,求证b1+b2+b3.bn
设数列{an}的前n项和为Sn,且满足S1=2,S(n+1)=3Sn+2(n=1,2,3) 设bn=2,S(n+1)=3Sn+2(n=1,2,3.) 注:n+1设数列{an}的前n项和为Sn,且满足S1=2,Sn+1=3Sn+2(n=1,2,3) 设bn=2,Sn+1=3Sn+2(n=1,2,3.)设bn=an比Sn平方,求证b1+b2+b3.bn
S(n+1)=3S(n)+2
所以S(n+1)=3[S(n)+1]
所以S(n)=S(1)*3^(n-1)=2*3^(n-1)
对于n>=2而言,有a(n)=S(n)-S(n-1)=2*3^(n-1)-2*3^(n-2)=4*3^(n-2)
所以b1=a1/(S1)^2=1/2
对于n>=2而言,有bn=an/(Sn)^2=3^(-n)=(1/3)^n
所以b1+b2+b3+...+bn
=1/2+(1/3)^2+(1/3)^3+...+(1/3)^n
=1/2+(1/3)^2*[1-(1/3)^(n-1)]/(1-1/3)
=1/2+1/6*[1-(1/3)^(n-1)]
=2/3-1/6*(1/3)^(n-1)
不知道哦。。。。。。。。。。。