CPM Homework Help : CALC Problem 12-109

Write the power series representation for $f(x) =\operatorname{ln}(10-x)$ then decide for what values of $x$ the series will converge.

Hint:

$\text{The power series for }f(x)\text{ is }\int-\frac{1}{10}\Big(1+\frac{x}{10}+\big(\frac{x}{10}\big)^2+...\Big)dx.$
$\text{Ratio Test: } \lim\limits_{n\to\infty}\Bigg|\frac{\Big(\frac{x}{10}\Big)^{n+2}\Big(\frac{1}{n+1}\Big)}{\Big(\frac{x}{10}\Big)^{n+1}\Big(\frac{1}{n}\Big)}\Bigg|$