数列{an}中,a1=0,a2=2,a(n+2)-6a(n+1)+5an=2^n,求an(n+2),(n+1)均为下标
问题描述：
数列{an}中,a1=0,a2=2,a(n+2)-6a(n+1)+5an=2^n,求an
(n+2),(n+1)均为下标
答
我提示你一下：
a(n+2)-6a(n+1)+5an=[a(n+2)-a(n+1)]-5[a(n+1)-a(n)]=2^n
将1中的式子累加，即可得到结果
答
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]...