Difference Series

First of all, please take a close look at the image above and analyze what's going on out there. I had discovered it accidentally in the year 2005, while playing with numbers (when I was in 3rd Grade). As you can clearly see in the image, there is a definite pattern to what happens in the successive difference series. I want a proof for my conjecture that for $$n$$th powers, the constant terms obtained would be $$n!$$. Please post the complete solution, if you have proved it.

Note by Satyajit Mohanty
2 years, 11 months ago

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Check this out. Just as Agnishom Chattopadhyay had mentioned the other day.

- 2 years, 11 months ago

- 2 years, 11 months ago

Hmm.. This was so easy. I just couldn't think of induction :/

- 2 years, 11 months ago

Oops the same link. Lol

- 2 years, 11 months ago