I'm not sure of the uses of the following equation, but either way it's quite novel and the proof quite nice because in mathematics the factorial function, f(x) = x!, can be quite frustrating sometimes. Using it often results in using the Gamma function which is getting into mathematics quite a bit beyond Joe Bloggs. Anyway, after stumbling across the following and proving it, then realising someone had already done it and getting over the disappointment of finding out I hadn't discovered something new in maths, I've written a nice, neat version of my findings:
Again, if you have any questions on the maths used or if you like to know more about the LaTeX used, or have anything suggestions on extensions or improvements of this proof, just leave a comment.
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