This is to get the limit as n approaches ∞
In the book this became a fraction somehow. There is probably some algebraic property that I am oblivious of. My prediction is that in 30 minutes I will refresh this page and say "OMG so obvious"
Thank you mister fantastic; that answer looks very good. What I'm still not entirely sure of was what compelled you to multiply by
I mean, obviously it is mathematically sound and allowed you to get the answer but I'm just not following the train of thought that had you multiplying by that exact ratio in the first place.