Question

这道题怎么做（数列）

Answer 1

an= (1/2)(a(n-1)+a(n-2))
an-a(n-1) = (-1/2)(a(n-1)-a(n-2))
[an-a(n-1)]/(a(n-1)-a(n-2)) = (-1/2)
[an-a(n-1)]/(a2-a1) = (-1/2)^(n-2)
an-a(n-1) = (-1/2)^(n-2)
(an-a(n-1)) +(a(n-1)-a(n-2))+ ..(a2-a1) = (-1/2)^0 +(-1/2)^1+...+(-1/2)^(n-2)
an-a1 = [1-(-1/2)^(n-1)]/(1+1/2)
an = a1+(2/3)(1-(-1/2)^(n-1))
= (2/3)[5/2- (-1/2)^(n-1)]
an/(an+1) = [5/2- (-1/2)^(n-1)]/[5/2- (-1/2)^(n)]
n->无穷
an/(an+1) = 1