Given is the following series

[![seq](https://i.stack.imgur.com/NYTAc.jpg)](https://i.stack.imgur.com/NYTAc.jpg)

I want to calculate the limit for $n \to \infty$.

I already recognised the geometric series $\sum\_{i=2}^n a^{i} = \frac{1}{1-a}$ for $a=e^\rho$ (since rho is supposed to be negative and $e^\rho$ muss be <1), but I am confused with $i-1$ in the exponent.

I changed the expression to:

$lim\_{n\to \infty} 2+\frac {-e^\rho+(e^\rho)^n}{-1+e^\rho}$ but can't find a way to express the limit just in term of rho.