Answer
$$\rho = 1$$
Work Step by Step
1. Use the ratio test to test for convergence:
$$\lim_{n \longrightarrow \infty}
\Bigg| \frac{ (x-3)^{n+1} }{ (x-3)^n } \Bigg |
= \lim_{n \longrightarrow \infty} \Bigg| x - 3 \Bigg| = x - 3$$
- Therefore, the series converges absolutely when $x - 3\lt 1$
$$\rho = 1$$
