If a power series satisfies with

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

Problem

If a power series

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

satisfies

\displaystyle\lim_{n\to\infty}\left|\frac{a_{n+1}}{a_n}\right| = L

with

L>0

, which expression gives the radius of convergence

R

of the series? (a)

R=L

(b)

R=L^{2}

(c)

R=\dfrac{1}{L}

(d)

R=\dfrac{1}{\sqrt{L}}