Determine the elementary function represented by the power series for all real .

MATHEMATICS · Single correct · AP · Calculus BC · Infinite Sequences and Series · Infinite Sequences and Series

Problem

Determine the elementary function represented by the power series

\displaystyle \sum_{n=0}^{\infty}\dfrac{(-1)^n (x^{2})^{n}}{n!\,2^{n}}

for all real

x

. (a)

e^{\,x^{2}/2}

(b)

e^{-x^{2}/2}

(c)

\cos\!\left(\dfrac{x^{2}}{2}\right)

(d)

e^{-x^{2}}