I hope this is the right forum (I new this board)

I've tried all sorts to prove the formula for the volume of a hyper-shere (not just for whole numbers, in case you're wondering I've seen mention that the max volume for a Hyper-sphere doesn't happen in a whole number of dimensions)

I've also searched the internet but all it does is give me the formula (I want the proof!)

Can someone help me on this? I would be very grateful.