Mathematics

Problem

In an infinite geometric progression with first term

a

and common ratio

r

(

|r|<1

), let

S_n

be the sum of the first

n

terms and

S_\infty

be the sum to infinity. Which of the following expressions equals the remainder

R_n = S_\infty - S_n

? a)

\dfrac{a r^{n+1}}{1 - r}

\dfrac{a(1 - r^{n})}{1 - r}

\dfrac{a r^{n}}{1 - r}

\dfrac{a r^{n-1}}{1 - r}