Answer
$\frac{4}{11}$
Work Step by Step
$0.363636...=0.36+0.0036+0.000036+...=0.36(0.01)^0+0.36(0.01)^1+0.36(0.01)^2+...$
$a_1=0.36$
$r=\frac{a_1}{a_2}=\frac{0.36(0.01)^2}{0.36(0.01)^0}=0.01$
$0.363636...=S=\frac{a_1}{1-r}=\frac{0.36}{1-0.01}=\frac{0.36}{0.99}=\frac{4}{11}$
