Question

型如a(n+1)=kan+b^n的数列如何求解

Answer 1

设a(n+1)+A*b^(n+1)=k(an+Ab^n),A为待定系数,由kA-Ab=1,得A=1/(k-b),数列{an+Ab^n}是公比为k的等比数列,故an+A*b^n=(a1+Ab)*k^(n-1),∴an=[a1+b/(k-b)]*k^(n-1)-b^n/(k-b).