In the situation where differences between consecutive squares, (or consecutive cubes, consecutive x^4, etc.) are calculated,(adsbygoogle = window.adsbygoogle || []).push({});

then the differences between those differences are calculated, and then the differences of those differences, and so on until you reach a constant number at a deep enough level,

which is equal to n! (n being the exponent that produced the initial numbers)

Is there some type of proof or explanation why it happen to be a factorial value?

Is it involved with calculus, since it is similar to transforming a function into a derivitive function, and continuing to find the derivitive?

Example:

F(x)=x^5

F'(x)=5x^4

F''(x)=5*4x^3

F'''(x)=5*4*3x^2

F''''(x)=5*4*3*2x

F'''''(x)=5*4*3*2*1=120=5!

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# Explanation of ultimate factorial value in differences between x^n integer series

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