When a power series centered at is integrated term by term to produce an antiderivative

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

Problem

When a power series centered at

a

is integrated term by term to produce an antiderivative, what happens to the radius of convergence of the resulting series? (a)

R_{\text{new}} = 2R

(b)

R_{\text{new}} = \dfrac{R}{2}

R_{\text{new}} = R

(d) The radius cannot be determined without analyzing each term.