series of differences: if we take a series of natural numbers to the power of N....

[ghsuturi]

Hello, first of all, I'm not sure this is the right forum for this question, so if it isn't I apologize in advance.
And now to the question itself:
I have a hypothesis that: if we take a series of natural numbers to the power of N, and create a series of differences from it over and over again, in the end we will reach a series where all the numbers are equal to each other and equal to N Factoria. Additionally, my hypothesis says that we will get this series after generating N series.
I proved this hypothesis for N equal to 1,2,3. Apparently if I sit on it long enough I can prove it for many individual cases, but it takes a lot of time, and in addition it will never be enough for a proof for all cases.
Do any of you know anything that might help me on the way to solving this?
PS, I don't speak English as a native language, so I use Google Translate to write (I can read in English). My native language is Hebrew.

 

[lookagain]

I have a hypothesis that: if we take a series of > > natural numbers < < to the power of N, and create a series of differences ...

You mean a sequence of consecutive positive integers.

 

[blamocur]

You hypothesis is correct (assuming @lookagain's clarification), and you can prove it using mathematical induction by N. BTW, your observation is analogous to the fact that [imath]\frac{\partial^n}{dx^n} x^n = n![/imath]