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On one of my calculus lectures I've seen the lecturer write:

$$(1+p)^n=1+np+\frac{n(n-1)}{2}p^2+\cdots+p^n$$

Could you please explain to me how did he get this equation?

Thank you very much.

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    As your title indicates, he used the [Binomial Theorem.](http://en.wikipedia.org/wiki/Binomial_theorem) The link supplies a proof. It is the proof that you have difficulty with?2012-04-02
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    yes, I guesses he used the Binomial Theorem, but doesn't the Binomial Theorem looks a bit different than this?2012-04-02
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    If you expand the expressions on the Binomial theorem, you should get those numbers.2012-04-02
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    What does the binomial theorem look like if you spell out each coefficient instead of using fancy notation like $\binom{n}{i}$?2012-04-02
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    @Anonymous: Different?2012-04-02
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    In the Wikipedia version, put $x=1$ and $y=p$.2012-04-02
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    Sorry for the question, after applying it with x=1 and y=p I got the same equation. Sorry and thanks again.2012-04-02

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