Apparently, there are two methods of solving this probability problem. The first, using p(n) = 1 - (365^n falling / 365^n) makes sense to me; however, there is an alternate solution using the Taylor series of e^x.

Here's the full solution on Wikipedia:

Birthday problem - Wikipedia, the free encyclopedia

I got lost at the transition from

http://upload.wikimedia.org/math/7/4...c4ca4959f8.png

to

http://upload.wikimedia.org/math/d/9...c059edb90e.png

What's happening here?