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# binomial expanison help watch

1. heyy,
can anyone help me on this qs please :
in the binomial expression of (2k + x) ^ n where k is a constant and n is a positive integer, the coefficient of x^2 is equal to the coefficient of x^3
prove n = 6k + 2

so heres what i got up to (not far!)...i apologise in advance if its not very clear

(n/2) (2k) ^ (n-2) x^2 = (n/3) (2k) ^ n-3 x^3

thanks
2. I take it by n/2 and n/3 you mean the binomial coefficients and ?

Basically, you're on the right lines, but your equation shouldn't have the bits in there (it's the coefficient, not the whole term). A good first step would be to put the binomial coefficients in terms of factorials; a lot of things will cancel out.

Basically you have
3. (Original post by nuodai)
I take it by n/2 and n/3 you mean the binomial coefficients and ?

Basically, you're on the right lines, but your equation shouldn't have the bits in there (it's the coefficient, not the whole term). A good first step would be to put the binomial coefficients in terms of factorials; a lot of things will cancel out.

Basically you have

haha yes i did mean that...dont no how to do the fancy writing on here .... why dont i put the x's in ? and ive not been taught it ur way, like we've been taught how to use the ( 1 + x) ^ n using factorials, but dont know hot to adjust this when its not 1 at the start (if that makes sense) do you know how i could still get the answer with my working minus the x's.... thankyou for your help as well
4. (Original post by _anum)
haha yes i did mean that...dont no how to do the fancy writing on here

See http://www.thestudentroom.co.uk/wiki/LaTex
It's well worth learning, and easy to pick up.

.... why dont i put the x's in ?
You don't need the x's as you are only interested in the coefficients of the terms. For example if you had then the coefficient of is just .

and ive not been taught it ur way, like we've been taught how to use the ( 1 + x) ^ n using factorials, but dont know hot to adjust this when its not 1 at the start (if that makes sense)
You may find this useful http://en.wikipedia.org/wiki/Binomial_theorem.
If not, just try googling binomial theorem

do you know how i could still get the answer with my working minus the x's.... thankyou for your help as well
See Nuodai's equation, and start cancelling down. Almost everything will cancel out and the terms you are left with can be manipulated into the desired equation.
5. (Original post by ghostwalker)
See http://www.thestudentroom.co.uk/wiki/LaTex
It's well worth learning, and easy to pick up.

You don't need the x's as you are only interested in the coefficients of the terms. For example if you had then the coefficient of is just .

You may find this useful http://en.wikipedia.org/wiki/Binomial_theorem.
If not, just try googling binomial theorem

See Nuodai's equation, and start cancelling down. Almost everything will cancel out and the terms you are left with can be manipulated into the desired equation.

aww thankyou so much for all that
the whole coefficient thing has just clicked
will try that n see if i get the answer after searching around how to do it! ...
thanks a lot for that
6. (Original post by nuodai)
I take it by n/2 and n/3 you mean the binomial coefficients and ?

Basically, you're on the right lines, but your equation shouldn't have the bits in there (it's the coefficient, not the whole term). A good first step would be to put the binomial coefficients in terms of factorials; a lot of things will cancel out.

Basically you have

okay now looked in my book (so ignore my last post!) and i have been taught that way( just me being stupid ) ... i understand how you got the equation but i still dont know how to solve it... i cant see how anything cancels out? sorry to be a pain
7. (Original post by _anum)
okay now looked in my book (so ignore my last post!) and i have been taught that way( just me being stupid ) ... i understand how you got the equation but i still dont know how to solve it... i cant see how anything cancels out? sorry to be a pain
I find that hard to believe. Have a think about it. Don't be overwhelmed by what you see; look at the detail.

1) What "bits" are the same on each side?

2) The (2k) terms are related in a structure similar to:

You should know how to solve that sort of equation?

3) How do you expand a factorial? Or what's, for example n!/(n-1)!
8. okay..... thankyou for your help

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