Binomial Past HSC (1 Viewer)

[mreditor16]

So I am trying to do this Q:



and the markers said this:



So, so far, I have done a separate expansion of both (1-x)^n AND (1 + 1/x)^n, as well as an expansion of (1-x)^n * (1 + 1/x)^n.

And I can see from looking at the first expansion, that I need to compare coefficients of x^2, but for the expansion of (1-x)^n * (1 + 1/x)^n, I can't see how to determine the coefficient of x^2, with n's in every coefficient..... :/

and also the marking notes mentions something about distinguishing between odd and even n - where does this come into play??

Thanks a lot guys! Most appreciated

 

[mreditor16]

This Q is from 1999, if anyone needed to know.

 

[faisalabdul16]

So I am trying to do this Q:



and the markers said this:



So, so far, I have done a separate expansion of both (1-x)^n AND (1 + 1/x)^n, as well as an expansion of (1-x)^n * (1 + 1/x)^n.

And I can see from looking at the first expansion, that I need to compare coefficients of x^2, but for the expansion of (1-x)^n * (1 + 1/x)^n, I can't see how to determine the coefficient of x^2, with n's in every coefficient..... :/

and also the marking notes mentions something about distinguishing between odd and even n - where does this come into play??

Thanks a lot guys! Most appreciated

I don't get what you mean by the bold part.

Because they're both to the power of n you can combine them into one fraction?

<img src="http://latex.codecogs.com/gif.latex?(\frac{1-x^{2}}{x})^{n}&space;\\&space;(\frac{1}{x}-x)^{n}&space;\\&space;$And&space;then&space;coefficient&space;of&space;x^{2}" title="(\frac{1-x^{2}}{x})^{n} \\ (\frac{1}{x}-x)^{n} \\ $And then coefficient of x^{2}" />

 

[mreditor16]

lol Drongoski, I see you lurking. some help please, my pal?

 

[mreditor16]

I don't get what you mean by the bold part.

Because they're both to the power of n you can combine them into one fraction?

<img src="http://latex.codecogs.com/gif.latex?(\frac{1-x^{2}}{x})^{n}&space;\\&space;(\frac{1}{x}-x)^{n}&space;\\&space;$And&space;then&space;coefficient&space;of&space;x^{2}" title="(\frac{1-x^{2}}{x})^{n} \\ (\frac{1}{x}-x)^{n} \\ $And then coefficient of x^{2}" />

try the question and get it out, then come back to me. you'll understand what I mean when you actually try to fully work through the Q.

 

[Drongoski]

Try, since k-(n-k) = 2, k = (n+2)/2:



(n+1)/2 is integer only for n even.

 

[mreditor16]

Try, since k-(n-k) = 2, k = (n+2)/2:



(n+1)/2 is integer only for n even.


ps: I have 2 separate tutoring lessons this afternoon, and need time to prepare. So didn't feel I've enough time to work on this.

thanks anyway drongoski!

anyone else?

 

[Kurosaki]

That's how I believe I did this question.

 

[mreditor16]

bump bump!

Carret? Trebla?

thanks those who have posted so far

 

[rumbleroar]

Have you tried equating the coefficients of anything?

 

[mreditor16]

bumpity bump!

 

[mreditor16]

Have you tried equating the coefficients of anything?

yes, refer to original post

 

[mreditor16]

Try, since k-(n-k) = 2, k = (n+2)/2:



(n+1)/2 is integer only for n even.

thanks heaps man! this is exactly what I needed. thanks a lot

 

[mreditor16]

What about if n is odd? The expression would be zero if n is odd unless someone's already pointed this out.

yep noted!