I have to prove that a generating function for the sequence $\{a_k\}$ where $a_k = (-8)^k$ for all integers $k\geq 0$ is $\cfrac{1}{1+8x}$. But I don't have any information on what $x$ is. Nor is there a $\sum$ in front of $a_k$ or the fraction $\dfrac{1}{1+8x}$.
Is this $x$ meant to be $k$? Meaning typographical error by the lecturer?
My question: Is this problem solvable? Please don't show me how to solve it if it is, as it is an assignment question. Some explanation would be nice though, and definitely a yes/no it is solvable.
An ordinary generating function $f(x)$ for a sequence $\{a_k\}_{k=0}^\infty$ satisfies the relationship $$f(x) = \sum_{k=0}^\infty a_k x^k.$$ Thus, substitute $a_k = (-8)^k$ and evaluate the resulting sum, which is a geometric series with common ratio $-8x$.