Exercise 6 Page 439

Consider the given infinite geometric series. Let's start by finding the partial sums $S_n$ for $n=1,$ $2,$ $3,$ $4,$ and $5.$ To calculate the partial sum $S_n,$ we need to add the first $n$ terms.

$n$	Calculations	$S_n$
$1$	$-$	$2$
$2$	$2+\frac{2}{6}$	$\frac{14}{6}$ $\approx$ $2.33$
$3$	$2+\frac{2}{6}+\frac{2}{36}$	$\frac{86}{36}$ $\approx$ $2.39$
$4$	$2+\frac{2}{6}+\frac{2}{36}+\frac{2}{216}$	$\frac{518}{216}$ $\approx$ $2.40$
$5$	$2+\frac{2}{6}+\frac{2}{36}+\frac{2}{216}+\frac{2}{1296}$	$\frac{3110}{1296}$ $\approx$ $2.40$