Suppose converges for

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

Problem

Suppose

\sum_{n=0}^{\infty} a_n x^{n}

converges for

|x|<4

and diverges for

|x|>4

. For which values of

x

is the series

\displaystyle \sum_{n=0}^{\infty} a_n x^{2n}

guaranteed to converge? (a)

|x|<4

(b)

|x|<8

(c)

|x|<2

(d)

|x|<\sqrt{2}