I wish to find the radius of convergence for
$$\sum_{n=0}^\infty \cos(in)z^n $$ that is $\sum_{n=0}^\infty \cosh(n)z^n $
but when i use the Cauchy-Hadamard theorem i get stuck with:
$$ \limsup_{n\to\infty} \sqrt[n]{\cosh(n)}=\limsup_{n\to\infty} \sqrt[n]{\frac{e^n+e^{-n}} 2}$$ but i don't know how to evaluate this
I also tried $$\lim_{n\to\infty} \frac{\left|\cosh(n+1)\right|}{\left|\cosh(n)\right|}<1$$
but I just get stuck with
$$\frac{|ee^n+\frac{1}{e}e^{-n}|}{|e^n+e^{-n}|}<1 $$
how do I find the radius of convergence if this series?