1. Assume we already have infinite precision right now.
2. A halving period is 210,000 blocks.
3. The first halving period produced 50 bitcoins per block, (50*210,000 total).
4. Each period is half the previous one.
5. http://www.wolframalpha.com/input/?i=sum+210000*50%2F2^n%2C+n%3D0+to+infinity

Or are you worried about the impact of rounding errors (which shouldn't be a problem given that we're not using floating point calculations)?