For which real values of does the series converge?

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

Problem

For which real values of

k

does the series

\displaystyle \sum_{n=0}^{\infty} (k-1)^{n}

converge? (a)

k<0\text{ or }k>2

(b)

-1<k<1

(c)

0<k<2

(d)

0\le k\le 2