The partial sums of a series are

MATHEMATICS · Subjective · AP · Calculus BC · Infinite Sequences and Series · Infinite Sequences and Series

Problem

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

, where

r

is a real constant with

r\ne1

. Determine all real values of

r

for which the series converges and state the corresponding sum

S

in terms of

r