- #1
ershi
- 4
- 0
In the situation where differences between consecutive squares, (or consecutive cubes, consecutive x^4, etc.) are calculated,
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!
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!