For this question, I'm stuck on finding the radius of convergence and interval of convergence for the power series. Here is what I have so far. Can anyone please help me out?
Find the radius of convergence and the interval of convergence for the power series.
$$\sum_{n=3}^{\infty} \frac{(x-1)^n}{n \sqrt{ln(n)}}$$
$\lim_{ n \to \infty} |\frac{c_{n+1}(x-a)^{n+1}}{c_n (x-a)^n}|$
= $\lim_{ n \to \infty}|\frac{(x-1)^{n+1}}{(n+1)\sqrt{ln(n+1)}} * \frac{n \sqrt{ln(n)}}{(x-1)^n}|$
= $\lim_{ n \to \infty}| \frac{(x-1)}{(n+1)\sqrt{ln(n+1)}} * n\sqrt{ln(n)}|$