For the series

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

Problem

For the series

\displaystyle\sum_{k=1}^{\infty} \frac{3^{k}(x-1)^{k}}{k}

, determine its interval of convergence. (a)

(\tfrac{2}{3},\,\tfrac{4}{3}]

(b)

(\tfrac{2}{3},\,\tfrac{4}{3})

(c)

\left[\tfrac{2}{3},\,\tfrac{4}{3}\right)

(d)

(-\tfrac{1}{3},\,\tfrac{1}{3})