Answer
$S=\frac{13}{9}=1.444...$
Work Step by Step
$\displaystyle \sum_{k=1}^{∞}1.3(\frac{1}{10})^{k-1}=1.3(\frac{1}{10})^0+1.3(\frac{1}{10})^1+1.3(\frac{1}{10})^2+...$
$a_1=1.3(\frac{1}{10})^0=1.3$
$r=\frac{a_2}{a_1}=\frac{1.3(\frac{1}{10})^1}{1.3(\frac{1}{10})^0}=\frac{1}{10}$
$S=\frac{a_1}{1-r}=\frac{1.3}{1-\frac{1}{10}}=\frac{1.3}{\frac{9}{10}}=\frac{13}{9}=1.444...$
