Q:

What's the limit of coefficient ratio  for a reciprocating power series?

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 $0<ck_i<1$ for any $i>0$. Define
$$
g=1+\sum_{i=1}^\infty t_ix^i,
$$
and 
$$
fg=1,
$$ 
i.e., $g$ is the inverse of power series $f$. 
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.

A:

As I explained in this answer to an earlier question of yours, $g$ will have a positive radius of convergence, determined by the location of the complex zero of $f$ closest to the origin (provided such a zero exists within the disk where the series for $f$ converges). This radius of convergence is in general quite unrelated to the radius of convergence $z_0$ of $f$ itself.

