Consider the infinite series

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

Problem

\displaystyle \sum_{n=1}^{\infty} \dfrac{(-3k)^{\,n+1}}{2^{2n}}

. For which real values of

k

does this series converge? (a)

|k|<\dfrac{2}{3}

(b)

|k|<\dfrac{4}{3}

(c)

|k|>\dfrac{4}{3}

(d)

0<k<\dfrac{3}{4}