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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:

The coefficients follow and

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

Completely stuck - just a hint required, am I on the right tracks with looking at series for the Pascal's Triangle sequences?

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2. Just a point: They aren't asking to prove a relationship between the second and third coefficients. They're asking to prove it between the and .
3. Does that mean induction?
4. (Original post by Gmart)
Does that mean induction?
that looks promising.
5. (Original post by Gmart)
Does that mean induction?
I don't think you need to go that far. You can use the formula for the binomial expansion, I think it has to do with the formula for .
6. (Original post by EricPiphany)
I don't think you need to go that far. You can use the formula for the binomial expansion, I think it has to do with the formula for .
(Original post by Gmart)
Does that mean induction?
I concur with this, just use the factorial definition of (I may have written that down incorrectly, so just check to be sure)
7. So the a vale takes care of itself, but the fraction I have down to:

But what is my next step? I need:

8. (Original post by Gmart)
So the a vale takes care of itself, but the fraction I have down to:

But what is my next step? I need:

Coefficient of rth term:

Coefficient of (r+1)th term:

So, what can you say about ?
9. Thank you so much
10. (Original post by Gmart)
Thank you so much
Very welcome.
11. (Original post by Zacken)
Very welcome.
Which module is this from?

Posted from TSR Mobile
12. (Original post by anoymous1111)
Which module is this from?

Posted from TSR Mobile
This is IB - but it's C1/2 knowledge.
13. (Original post by Zacken)
Coefficient of rth term:

Coefficient of (r+1)th term:

So, what can you say about ?
Where do I go from here?

Posted from TSR Mobile
14. (Original post by anoymous1111)
Where do I go from here?

Posted from TSR Mobile
Simplify the quotient of factorials.

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