Consider the power series P(x)= _ n=1 ^ n! n^ n ,(x-2)^ n
MATHEMATICS · Multi-part · AP · Calculus BC · Infinite Sequences and Series · Infinite Sequences and Series
Problem
Consider the power series
P(x)=n=1∑∞nnn!(x−2)n.
Respond to each of the following prompts.
(1) Determine the radius of convergence R of P(x).
(2) Identify all real numbers x for which the series converges absolutely.
(3) Analyze the behavior of the series at each endpoint of the interval found in part (b) and state the complete interval of convergence, justifying your conclusions.