Chapter 6.1, Problem 56E

In the following exercises, suppose that $p(x)=$ ${\displaystyle \underset{n=0}{\overset{\infty }{\sum }}{a}_n{x}^n}$ Satisfies $\underset{n\to \infty }{\lim }$

$\frac{a_n+1}{a_n}=1$ where $a_n\ge 0$ for each $n$ . State whether each series converges on the full interval (− 1, 1), or if there is not enough information to draw a conclusion. Use the comparison test when appropriate.

56. Suppose that $p(x)$is a polynomial of degree N. Find the radius and interval of convergence of ${\displaystyle \underset{n=1}{\overset{\infty }{\sum }}p(n)x^n}$ .