Question 13
Use the root test to find the radius of convergence for
$\sum_{n=1}^{\infty} (n^n - 1)^n x^n$.
Question 14
Suppose that $p(x) = \sum_{n=0}^{\infty} a_n x^n$ converges on $(-1, 1]$, find the interval of convergence of $p(8x - 5)$.
x = _____, left end included (enter Y or N): _____
to x = _____, right end included (enter Y or N): _____
Question 15
In the following exercises, suppose that $p(x) = \sum_{n=0}^{\infty} a_n x^n$ satisfies $\lim_{n \to \infty} \frac{a_{n+1}}{a_n} = 1$ where $a_n \ge 0$
for each $n$. State whether each series $\sum_{n=0}^{\infty} a_n 2^n$ converges on the full interval $(-1, 1)$, or if there is not
enough information to draw a conclusion. Use the comparison test when appropriate.
Not enough information
Converges on the full interval $(-1, 1)$
