数列满足2Sn=A(n+1) -2^(n+1)+1” 如何证明{an+2的n次方}为等比数列
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数列满足2Sn=A(n+1) -2^(n+1)+1” 如何证明{an+2的n次方}为等比数列
![数列满足2Sn=A(n+1) -2^(n+1)+1” 如何证明{an+2的n次方}为等比数列](/uploads/image/z/20312828-44-8.jpg?t=%E6%95%B0%E5%88%97%E6%BB%A1%E8%B6%B32Sn%3DA%EF%BC%88n%2B1%EF%BC%89+-2%5E%EF%BC%88n%2B1%EF%BC%89%2B1%E2%80%9D+%E5%A6%82%E4%BD%95%E8%AF%81%E6%98%8E%7Ban%2B2%E7%9A%84n%E6%AC%A1%E6%96%B9%7D%E4%B8%BA%E7%AD%89%E6%AF%94%E6%95%B0%E5%88%97)
2Sn = a(n+1) -2^(n+1) +1
an = Sn -S(n-1)
2an =a(n+1) -2^(n+1) - [an -2^n]
a(n+1) = 3an + 2^n
a(n+1) + 2^(n+1) = 3[ an + 2^n ]
=>{an + 2^n} 是等比数列,q=3
an = Sn -S(n-1)
2an =a(n+1) -2^(n+1) - [an -2^n]
a(n+1) = 3an + 2^n
a(n+1) + 2^(n+1) = 3[ an + 2^n ]
=>{an + 2^n} 是等比数列,q=3
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