A1=2 ,A(n+1)=2An+2^n 求An.
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A1=2 ,A(n+1)=2An+2^n 求An.
A1=2 ,A(n+1)=2An+2^n 求An.
A1=2 ,A(n+1)=2An+2^n 求An.
两边同时除以2^n得:
A(n+1)/2^n =2An/2^n +1
A(n+1)/2^n -An/2^(n-1)=1
A(n+1)/2^(n+1)-An/2^n=1/2
∴{An/2^n}为首项是1,公差为1/2的等差数列
∴An/2^n=1+(n-1)*1/2=1/2n+1/2
∴An=(n+1)*2^(n-1)
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