已知数列{An}满足A1=1,A2=3,A(n+2)=3A(n+1)-2An (n∈整数)证明数列{A(n+1)-An}是等比数列?求数列An通项公式?
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![已知数列{An}满足A1=1,A2=3,A(n+2)=3A(n+1)-2An (n∈整数)证明数列{A(n+1)-An}是等比数列?求数列An通项公式?](/uploads/image/z/5196414-30-4.jpg?t=%E5%B7%B2%E7%9F%A5%E6%95%B0%E5%88%97%EF%BD%9BAn%EF%BD%9D%E6%BB%A1%E8%B6%B3A1%3D1%2CA2%3D3%2CA%28n%2B2%29%3D3A%28n%2B1%29-2An+%28n%E2%88%88%E6%95%B4%E6%95%B0%EF%BC%89%E8%AF%81%E6%98%8E%E6%95%B0%E5%88%97%EF%BD%9BA%28n%2B1%29-An%EF%BD%9D%E6%98%AF%E7%AD%89%E6%AF%94%E6%95%B0%E5%88%97%3F%E6%B1%82%E6%95%B0%E5%88%97An%E9%80%9A%E9%A1%B9%E5%85%AC%E5%BC%8F%3F)
已知数列{An}满足A1=1,A2=3,A(n+2)=3A(n+1)-2An (n∈整数)证明数列{A(n+1)-An}是等比数列?求数列An通项公式?
已知数列{An}满足A1=1,A2=3,A(n+2)=3A(n+1)-2An (n∈整数)
证明数列{A(n+1)-An}是等比数列?求数列An通项公式?
已知数列{An}满足A1=1,A2=3,A(n+2)=3A(n+1)-2An (n∈整数)证明数列{A(n+1)-An}是等比数列?求数列An通项公式?
证明:
详细证明请参见下图.
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