A power series has radius of convergence

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

Problem

A power series

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

has radius of convergence

R=3

. Which of the following statements about the transformed series

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

is correct? (a) It converges for

|x|<3

and diverges for

|x|>3

. (Radius

=3

) (b) It converges for

|x|<1.5

and diverges for

|x|>1.5

. (Radius

=1.5

) (c) It converges for

|x|<6

and diverges for

|x|>6

. (Radius

=6

) (d) It converges for

|x|<0.75

and diverges for

|x|>0.75

. (Radius

=0.75

)