数列an中 a1=0 a2=2 a(n+2)-6a(n+1)+5an=2^n 求通项an

问题描述:

数列an中 a1=0 a2=2 a(n+2)-6a(n+1)+5an=2^n 求通项an

1、设b[n]=a[n]+⅓×2^n,那么b[1] = a[1] + ⅓×2 = ⅔b[2] = a[2] + ⅓×2^2 = 10/3且有 a[n] = b[n] - ⅓×2^n,代入 a[n+2] - 6a[n+1] + 5a[n] = 2^n 并整理,有b[n+2] - 6b[n+1] + 5b[n]...