Answer
$\dfrac{4}{9}$
Work Step by Step
Here, we have $a_n= a_1 r^{n-1}$ for the Geometric series.
Re-arrange the given series as: $0.444...=0.4 +0.4 (0.1) +0.4 (0.1)^2 +....$
First term $a_1=0.4$ and Common ratio $r=0.1$
The sum of an infinite Geometric Series can be found using: $S_n=\dfrac{a_1}{1-r}$
Thus, $S_n=\dfrac{0.4}{1-0.1}$
Hence, $S_n=\dfrac{4}{9}$
