Let $d_n$ be the number of ordered sequences of die rolls (i.e., sequences of integers from $1$ to $6$) that add up to $n$. For example, $d_4=8$, because a total of $4$ can be rolled in $8$ ways:
$$\begin{array}{*4c} 4 & 3+1 & 2+2 & 1+3 \\ \\ ~2+1+1~ & ~1+2+1~ & ~1+1+2~ & ~1+1+1+1~ \end{array}$$ and $d_0=1$, since $0$ can be rolled in one way (roll no dice).
Let $D(x)$ be the generating function $$D(x) = d_0 + d_1x + d_2x^2 + d_3x^3 + \cdots .$$ Then $\frac 1{D(x)}$ is a polynomial. What polynomial is it?
I know for sure that $\frac{1}{D(x)}$ is referring to $\frac{1}{1-(x+x^2+x^3+x^4+x^5+x^6)}$ the geometric function. But I don't understand what to put as the answer?
I understand this is a duplicate question, but I don't understand how to translate and clarify.
If you "know for sure that $\frac{1}{D(x)}$ is referring to $\frac{1}{1-(x+x^2+x^3+x^4+x^5+x^6)}$" you should invert both sides and get $D(x)=1-(x+x^2+x^3+x^4+x^5+x^6)$