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.

## Comments

Sort by:

TopNewestCheck this out. Just as Agnishom Chattopadhyay had mentioned the other day. – Sudeep Salgia · 1 year, 3 months ago

Log in to reply

Method of Differences – Agnishom Chattopadhyay · 1 year, 3 months ago

Log in to reply

– Satyajit Mohanty · 1 year, 3 months ago

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

– Sudeep Salgia · 1 year, 3 months ago

Oops the same link. LolLog in to reply