For the power series with radius of convergence

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

Problem

For the power series

f(x)=\sum_{n=0}^{\infty} a_n (x-c)^n

with radius of convergence

R>0

, which statement best describes the radius of convergence of

f'(x)

? (a) It cannot be determined without additional information. (b) It is the same value

R

. (c) It equals

\dfrac{R}{2}

. (d) It equals

R^2