QuestionFind the interval of convergence for the series $\sum_{n=1}^{\infty} \frac{(x-1)^{n}}{3^{n}}$.

Studdy Solution
The series $\sum_{}^{\infty} \frac{(x-)^{n}}{3^{n}}$ converges absolutely for $x$ in the interval $(-2,4)$ and diverges at the endpoints $x = -2$ and $x =4$. Therefore, the interval of convergence is $(-2,4)$.
The interval of convergence of the series is $(-2,4)$.