Consider the series _ n=1 ^ (x+2)^ n 3^ n n

MATHEMATICS · Multi-part · AP · Calculus BC · Infinite Sequences and Series · Infinite Sequences and Series

Problem

Consider the series

\sum_{n=1}^{\infty}\frac{(x+2)^{n}}{3^{n}n}.

Answer the following. (1) Determine the radius of convergence

R

. (2) Find the interval of convergence, stating clearly whether the series converges, diverges, or converges conditionally at each endpoint.