数列An满足A1=2,An+1-An=3*2^2n-1.〔Ⅰ〕求数列An的通项公式;〔Ⅱ〕令Bn=nAn,求数列Bn的前n项和?
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![数列An满足A1=2,An+1-An=3*2^2n-1.〔Ⅰ〕求数列An的通项公式;〔Ⅱ〕令Bn=nAn,求数列Bn的前n项和?](/uploads/image/z/2981657-65-7.jpg?t=%E6%95%B0%E5%88%97An%E6%BB%A1%E8%B6%B3A1%3D2%2CAn%2B1-An%3D3%2A2%5E2n-1.%E3%80%94%E2%85%A0%E3%80%95%E6%B1%82%E6%95%B0%E5%88%97An%E7%9A%84%E9%80%9A%E9%A1%B9%E5%85%AC%E5%BC%8F%EF%BC%9B%E3%80%94%E2%85%A1%E3%80%95%E4%BB%A4Bn%3DnAn%2C%E6%B1%82%E6%95%B0%E5%88%97Bn%E7%9A%84%E5%89%8Dn%E9%A1%B9%E5%92%8C%3F)
数列An满足A1=2,An+1-An=3*2^2n-1.〔Ⅰ〕求数列An的通项公式;〔Ⅱ〕令Bn=nAn,求数列Bn的前n项和?
数列An满足A1=2,An+1-An=3*2^2n-1.〔Ⅰ〕求数列An的通项公式;〔Ⅱ〕令Bn=nAn,求数列Bn的前n项和?
数列An满足A1=2,An+1-An=3*2^2n-1.〔Ⅰ〕求数列An的通项公式;〔Ⅱ〕令Bn=nAn,求数列Bn的前n项和?
An-(An-1)=3*2^2n-3
(An-1)-(An-2)=3*2^2n-5
……
A2-A1=3*2^2
相加得
An-A1=3*2(1-4^n-1)/(1-4)
An-2=2*4^n-1-2
An=2*4^(n-1)=2^(2n-1)
Bn=n*2^(2n-1)
Sn=1*2^1+2*2^3+3*2^5+4*2^5……+n*2^(2n-1)
4Sn= 1*2^3+2*2^5+3*2^5……+(n-1)*2^(2n-1)+n*2^(2n+1)
错位相减得
-3Sn=2+2^3+2^5+2^7+……2^(2n-1)-n*2^(2n+1)
-3Sn=2/3(4^n -1)-)-n*2^(2n+1)
Sn=-2/9(4^n -1)+n/3*2^(2n+1)
题抄错了吧登时左边怎么会有2个An可以消掉的
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