设数列{An}满足A1+3A2+3²A3+******+3^(n-1)An=n/3
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设数列{An}满足A1+3A2+3²A3+******+3^(n-1)An=n/3
1、求{An}通项公式
1、求{An}通项公式
![设数列{An}满足A1+3A2+3²A3+******+3^(n-1)An=n/3](/uploads/image/z/5304714-42-4.jpg?t=%E8%AE%BE%E6%95%B0%E5%88%97%7BAn%7D%E6%BB%A1%E8%B6%B3A1%2B3A2%2B3%26sup2%3BA3%2B%2A%2A%2A%2A%2A%2A%2B3%5E%EF%BC%88n-1%EF%BC%89An%3Dn%2F3)
A1+3A2+3²A3++3^(n-1)An+3^n*A(n+1)=(n+1)/3
下减上:3^n*A(n+1)=1/3
A(n+1)=3^(-n-1)
则通项An=3^(-n)
下减上:3^n*A(n+1)=1/3
A(n+1)=3^(-n-1)
则通项An=3^(-n)
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