Consider the Maclaurin series for

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

Problem

e^{x^{2}}

, given by

V(x)=\sum_{n=0}^{\infty}\frac{x^{2n}}{n!}.

Respond to the following. (1) Determine the radius of convergence

R

V(x)

. (2) For

x=1

, decide whether the series converges absolutely, converges conditionally, or diverges. Provide justification. (3) For

x=2

, determine whether the series converges or diverges and support your conclusion with appropriate reasoning.