Mathematics

Problem

Consider the infinite series

\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}

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

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

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