Answer
$S_{6}$ = $1.24992$
Work Step by Step
$S_{1}$ = $1$
$S_{2}$ = $1+\frac{1}{5}$ = $\frac{6}{5}$ = $1.2$
$S_{3}$ = $1+\frac{1}{5}+\frac{1}{25}$ = $\frac{31}{25}$ = $1.24$
$S_{4}$ = $1+\frac{1}{5}+\frac{1}{25}+\frac{1}{125}$ = $\frac{156}{125}$ = $1.248$
$S_{5}$ = $1+\frac{1}{5}+\frac{1}{25}+\frac{1}{125}+\frac{1}{625}$ = $\frac{781}{625}$ = $1.2496$
$S_{6}$ = $1+\frac{1}{5}+\frac{1}{25}+\frac{1}{125}+\frac{1}{625}+\frac{1}{3125}$ = $\frac{3906}{3125}$ = $1.24992$
$1.25-1.24992$ = $0.00008$
