Question

一道数列题求解..特征根方程 ,我不是很懂 在自学.

Answer 1

a(n+1)-5an+6a(n-1)=0

a(n+1)-2an = 3(an-2a(n-1))

[a(n+1)-2an]/(an-2a(n-1)) =3

[a(n+1)-2an]/(a2-2a1) =3^(n-1)

a(n+1)-2an = -3^(n-1)

an-2a(n-1) =-3^(n-2)

an + (1/3).3^n = 2[ a(n-1) + (1/3).3^(n-1)]

[an + (1/3).3^n]/[ a(n-1) + (1/3).3^(n-1)] =2

[an + (1/3).3^n]/[ a2 + (1/3).3^2] = 2^(n-2)

an + (1/3).3^n = 2^n

an = 2^n-3^(n-1)