Mathematics

Problem

Consider the Maclaurin series for

e^{x^{2}}

, given by

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

Respond to the following. a. Determine the radius of convergence

R

V(x)

. b. For

x=1

, decide whether the series converges absolutely, converges conditionally, or diverges. Provide justification. c. For

x=2

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