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.

#Algebra

Easy Math Editor

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`2^{34}`	$2^{34}$
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Comments

Method of Differences

Agnishom Chattopadhyay - 5 years, 11 months ago

Oops the same link. Lol

Sudeep Salgia - 5 years, 11 months ago

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

Satyajit Mohanty - 5 years, 11 months ago

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

Sudeep Salgia - 5 years, 11 months ago

Math	Appears as
Remember to wrap math in `\(` ... `\)` or `\[` ... `\]` to ensure proper formatting.
`2 \times 3`	$2 \times 3$
`2^{34}`	$2^{34}$
`a_{i-1}`	$a_{i-1}$
`\frac{2}{3}`	$\frac{2}{3}$
`\sqrt{2}`	$\sqrt{2}$
`\sum_{i=1}^3`	$\sum_{i=1}^3$
`\sin \theta`	$\sin \theta$
`\boxed{123}`	$\boxed{123}$