In the ratio test applied to the power series

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

Problem

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

, the limit

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

is found to be a positive finite number. Which of the following gives the radius of convergence

R

in terms of

L

? (a)

R=L

(b)

R=\dfrac{1}{L^{2}}

(c)

R=\dfrac{1}{L}

(d)

R=L^{2}