Answer
$$\rho = 1$$
Work Step by Step
1. Use the ratio test to test for convergence:
$$\lim_{n \longrightarrow \infty}
\Bigg| \frac{ \frac{(x-x_0)^{n+1}}{n+1} }{ \frac{ (x-x_0)^n }{n} } \Bigg |
= \lim_{n \longrightarrow \infty} \Bigg| (x-x_0) \frac{n}{n+1} \Bigg| = x - x_0$$
- Therefore, the series converges absolutely when $x - x_0\lt 1$
$$\rho = 1$$
