Here's the general formula: (copy everything between angle brackets)

<http://texify.com/?$\frac{1}{10^n-m} = \sum_{i=0}^\infty \frac{m^i}{(10^n)^{i+1}}$>

And here's OP's result where n=4 and m=2:

http://www.wolframalpha.com/input/?i=%5Csum_%7Bi%3D0%7D%5E%5...