The th partial sum of a series is for a real constant

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

Problem

The

n

th partial sum of a series is

\displaystyle S_n=\frac{1- r^{\,n+1}}{1-r}

for a real constant

r\neq1

. Which of the following identifies the values of

r

for which the series converges? (a)

-1<r\le1

(b)

|r|<1

(c)

r<1

(d)

|r|>1