S_n = \displaystyle\sum_{k=1}^{\infty} (\displaystyle\frac{9}{10^k}) = 9\displaystyle\sum_{k=1}^{\infty} (\displaystyle\frac{1}{10})^k = 9*\lim_{n\to\infty}{\displaystyle\frac{\frac{1}{10} - \left(\frac{1}{10}\right)^{n+1}}{1 - \frac{1}{10}}} = 9 * \displaystyle\frac{\frac{1}{10}}{1 - \frac{1}{10}} = 1