Determine all real numbers for which the series converges.

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

Problem

Determine all real numbers

x

for which the series

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

converges. (a)

(-1,\,3)

(b)

[-1,\,3)

(c)

(-1,\,3]

(d)

[-1,\,3]