I have a question about the coefficient in the inverse of the power series.
Assume $ f=1-\sum_{i=1}^{\infty}(ck_i)x^i, $ where $c$ and $k_i$ are positive and $0
Now I know that if $\{k_i\}$ is geometric series, i.e., $k_i=k_1^i$, then $\{t_i\}$ are also geometric series. And I remember the common ratio is $c(k_1+1)$. (If it is wrong, please point out the mistakes, thanks.)
My question is, if we don't have the condition that $\{k_i\}$ is geometric series, but we assume $ \lim_{i\rightarrow\infty}\frac{k_{i+1}}{k_i}=z_0 $ is a positive constant and less than $1$. In this case, is $ \lim_{i\rightarrow\infty}\frac{t_{i+1}}{t_i} $ also a constant? If yes, what is it?
I don't know much about this. Can you help me? Thanks in advance.