The th partial sum of an infinite series is

MATHEMATICS · Single correct · A Level · Mathematics · Sequences and series · Sequences and series

Problem

The

n

th partial sum of an infinite series is

\displaystyle S_n = \frac{5\bigl(1 - r^{\,n+1}\bigr)}{1 - r}

, where

r

is a real constant with

r\neq1

. Which of the following pairs of conditions on

r

and corresponding series sums is correct? (a) Convergent for

|r|>1

with sum

\displaystyle\frac{5}{r-1}

. (b) Convergent for

|r|<1

with sum

5(1-r)

. (c) Convergent for

r<1

with sum

\displaystyle\frac{5}{1-r}

. (d) Convergent for

|r|<1

with sum

\displaystyle\frac{5}{1-r}