Question

Pprove that if m and n are positive integers, then

Answer 1

\[\sum_{k1+k2+....km=n}^{} \left(\begin{matrix}n\\k1, k2, ....,km\end{matrix}\right) = m^n\]

Answer 2

\[\left(\begin{matrix}n \\ k1,k2,...,km\end{matrix}\right)\]
?

Answer 3

can u give me a link

Answer 4

thats exactly what it looks like, i think its "choose numbers" multinomial coefficients kind of stuff.

Answer 5

\[(x _{1}+x _{2}+...+x _{m})^n=\sum_{k _{1}+k _{2}+...+k _{m}=n}^{} \left(\begin{matrix}n \\ k1,k2,...,km\end{matrix}\right) x_{1}^{k_{1}} x_{2}^{k_{2}} ... x_{m}^{k_{m}}\]

Answer 6

just let x1=x2=...=xm=1

Answer 7

I think I see what you're doing, but could you explain the left side and what your idea is.

Answer 8

Nevermind, I see it. I appreciate the work you've done, thank you.

Answer 9

that's The Multinomial theorem statement

Answer 10

this may help
http://en.wikipedia.org/wiki/Multinomial_theorem

Answer 11

your welcome