What is the R.O.C. of the following power series:
$\sum_{n\geq2}\frac{z^{n}}{\ln(n)}\qquad?$ Here is my attempt:
$\lim_{n\rightarrow\infty}\left|\frac {z^{n+1}\ln(n)}{\ln(n+1)z^{n}}\right|=\lim_{n\rightarrow\infty}\left|\frac{z\ln(n)}{\ln(n+1)}\right|=z$ so the R.O.C. = $\frac {1}{z}$. Is this right?