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已知A1=1,A(n+1)=2^n+3An,求其通项公式
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已知A1=1,A(n+1)=2^n+3An,求其通项公式
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令bn = an / 3^(n-1)
则b(n+1) = a(n+1) / 3^n = (2/3)^n + bn
bn = b1 + 2/3 + …… + (2/3)^(n-1)
=[1-(2/3)^n]/(1-2/3)
=3 - 3*(2/3)^n
an = 3^n - 2^n
则b(n+1) = a(n+1) / 3^n = (2/3)^n + bn
bn = b1 + 2/3 + …… + (2/3)^(n-1)
=[1-(2/3)^n]/(1-2/3)
=3 - 3*(2/3)^n
an = 3^n - 2^n
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