Infinite Sequences and Series (BC Only)

Considering a function represented by a power series $\sum_{n=0}^{\infty} a_n (x-1)^n$ converges absolutely at $x=3$, how would you describe its behavior at $x=-1$?

If the power series $\sum_{n=0}^{\infty} \frac{(2x+3)^n}{5^n}$ has a radius of convergence $R$, what is the interval of convergence for this series?

To find the radius of convergence for a power series, what must you first calculate from the general term $a_n$?

What is the interval of convergence of the power series represented by the function $f(x) = \sum_{n=0}^{\infty} \frac{(2x)^n}{n^2}$?

If the power series for $f(x) = \sum_{n=0}^{\infty} \frac{x^n}{n!}$ converges on its interval of convergence, what is the radius of convergence for the related series $g(x) = \sum_{n=0}^{\infty} \frac{(2x)^n}{n!}$?

If a power series converges absolutely at $x = a$, then it will also converge when $x$ equals what other value?

What is the interval of convergence of the power series represented by the function $f(x) = \sum_{n=1}^{\infty} \frac{(x-2)^n}{n^3}$?

Given a power series $\sum_{n=0}^{\infty} \frac{(x-3)^n}{2^n}$, using the Cauchy-Hadamard theorem as an alternative to the ratio test, what is the radius of convergence?

If the power series $\sum_{n=0}^{\infty} \frac{(3x)^n}{n!}$ has a radius of convergence $R$, what is the interval of convergence for this series?

If the interval of convergence for a power series is (-4, 6), what can be said about the radius of convergence?