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# Binomial Proof watch

1. So I have this question asking for a proof of a relationship between the second and third co-efficients of the Binomial Expansion:

are always equal to:

But how can I pull these together to one simple proof?

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2. (Original post by Gmart)
So I have this question asking for a proof of a relationship between the second and third co-efficients of the Binomial Expansion:

are always equal to:

But how can I pull these together to one simple proof?

and are not necessarily the second and third terms, they are simply two consecutive terms.
Spoiler:
Show
You know that:

What can you say about the coefficient of x^r?
Spoiler:
Show
Recall:
{n \choose r}=\dfrac{n!}{r!(n-r)!}
3. for some reason it won't let me edit the text in the above spoiler.
.
4. (Original post by joostan)
and are not necessarily the second and third terms, they are simply two consecutive terms.
Seems like a duplicate post to me, I've answered this question in a thread an hour or so ago.

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Updated: November 8, 2015
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