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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
1 year, 8 months ago

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Check this out. Just as Agnishom Chattopadhyay had mentioned the other day. Sudeep Salgia · 1 year, 8 months ago

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Method of Differences Agnishom Chattopadhyay · 1 year, 8 months ago

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@Agnishom Chattopadhyay Hmm.. This was so easy. I just couldn't think of induction :/ Satyajit Mohanty · 1 year, 8 months ago

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@Agnishom Chattopadhyay Oops the same link. Lol Sudeep Salgia · 1 year, 8 months ago

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