The coefficients of the power series $\Sigma^\infty_{k=0}a_kx^k$ satisfy this relation, $a_k+Aa_{k-1}+Ba_{k-2}=0$, where $k=2, 3, 4,...$

Question

I am having trouble with this question:

The coefficients of the power series $\Sigma^\infty_{k=0}a_kx^k$ satisfy this relation, $a_k+Aa_{k-1}+Ba_{k-2}=0$, where $k=2, 3, 4,...$

(a) Show that for $|x|<R$, the radious of convergence,

$(1+Ax+Bx^2)\Sigma^\infty_{k=0}a_kx^k=a_0+(a_1+Aa_0)x$

(b) Hence establish that,

$\Sigma^n_{k=0}x^k=\frac{1}{1-x}$ for $|x|<1$

Part b I was able to do using geometric series sum. However, I have no idea of what do to in part a. I would like if someone could give me a hint, not the full anwser, because I want to solve it.