Find the sum of $n$ terms of the series $0.6+0.66+0.666+......$

Question

$\begin{array}{1 1}\large\frac{2n}{3}-\frac{(10^n-1)}{27.10^n} \\\large\frac{2n}{3}-\frac{2(10^n-1)}{27.10^n} \\ \large\frac{2n}{3}-\frac{2(10^n-1)}{9.10^n} \\\large\frac{2n}{3}-\frac{(10^n-1)}{9.10^n} \end{array} $