Binomial identities (1 Viewer)

[deswa1]

Hey guys

Can one of you help with this question:

<a href="http://www.codecogs.com/eqnedit.php?latex=\textup{If }(1@plus;x)^n=c_{0}@plus;c_{1}x@plus;c_{2}x^2@plus;...@plus;c_{n}x^n\textup{, show that}\\ c_{0}c_{2}@plus;c_{1}c_{3}@plus;c_{2}c_{4}@plus;c_{n-2}c_{n}=\frac{(2n)!}{(n@plus;2)!(n-2)!}" target="_blank"><img src="http://latex.codecogs.com/gif.latex?\textup{If }(1+x)^n=c_{0}+c_{1}x+c_{2}x^2+...+c_{n}x^n\textup{, show that}\\ c_{0}c_{2}+c_{1}c_{3}+c_{2}c_{4}+c_{n-2}c_{n}=\frac{(2n)!}{(n+2)!(n-2)!}" title="\textup{If }(1+x)^n=c_{0}+c_{1}x+c_{2}x^2+...+c_{n}x^n\textup{, show that}\\ c_{0}c_{2}+c_{1}c_{3}+c_{2}c_{4}+c_{n-2}c_{n}=\frac{(2n)!}{(n+2)!(n-2)!}" /></a>

If you can be bothered to write a complete solution, that would be great but a hint should hopefully be enough.

Thanks again

 

[SunnyScience]

Have you tried (1+x)^n(1-x)^n expanding and then converting nCr = n!/r!(n-r)! ?

 

[Carrotsticks]

 

[deswa1]

Oh right- thanks guys

I didn't think of multiplying by (1+x)^n