Question

prove that C(2m,0)^3-C(2m,1)^3+C(2m,2)^3-...+C(2m,2m)^3=((3m)!/(m!)^3)*(-1)^m

Answer 1

\[C(n,k)= \left(\begin{matrix}n \\ k\end{matrix}\right)=n!/k!/(n-k)!\]

Answer 2

Could you please expand the series series properly where exactly are the minus signs? THe first two terms are positive how did the third become negative

Answer 3

the first item is positive, the second is negative and the third is positive again

Answer 4

I am not sure for cubes but for squares just multiply two series and observe coeffecients.

Answer 5

i have no idea, it is a really difficult problem

Answer 6

This is actually dixon's identity i'm not sure how to prove it.

Answer 7

oh..who is dixon? a mathematician?

Answer 8

yeah dude obvi just google it you shld find it.

Answer 9

yeah i find the identity, but not the proof

Answer 10

If google does not have it what are the chances that a teenager does?? :D :D

Answer 11

oh i find it
http://math.ecnu.edu.cn/~jwguo/maths/dixon.pdf