I have series when $n$ goes from $1$ to infinity $(z/\ln(in))^n$ and need to find the radius of convregence. I tried this
$1/R = \limsup ((1/\ln(in))^n)^(1/n)$ when $n \to \infty$ (Cauchy's rule),
$1/R = \limsup 1/(\ln i + \ln(n))$ when $n\to\infty$
$1/R = 1/\infty \implies R = \infty$
I'm not sure if $\lim\ln(n)=\infty$ when $n\to\infty$.