deswa1
Well-Known Member
- Joined
- Jul 12, 2011
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- HSC
- 2012
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
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