設A(n+1)+k(n+1)+h=3(A(n)+kn+h)
乘開,移項得A(n+1)=3A(n)+2kn+2h-k
跟原式比較係數可得k=1,h=-1/2
所以A(n+1)+1(n+1)-1/2=3(A(n)+1n-1/2)
A2+2-1/2=3(A1+1-1/2)
A3+3-1/2=3(A2+2-1/2)
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A(n)+n-1/2=3(A(n-1)+(n-1)-1/2)
全相乘,約分A(n)+n-1/2=3^(n-1)*(A1+1-1/2)=(3^n)/2
A(n)=(3^n-2n+1)/2
參考看看
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