Answer
$S_\infty=\frac{0.9}{1-0.1}=1$
Our intuition might say that the given will never be equal to 1.
Work Step by Step
The number $.0.9999..$ is the infinite sum of the geometric series with $a_1=0.9$ and with the ratio of $r=0.1$ (as given),
as $\mid r\mid <1$ the sum exists.
The sum of an infinite geometric series is:
$S_\infty=\frac{a_1}{1-r}$
Here:
$S_\infty=\frac{0.9}{1-0.1}=1$
Our intuition might say that the given will never be equal to 1.
