# Help with binomial theorem

1. Oct 28, 2009

### ipitydatfu

1. The problem statement, all variables and given/known data

prove that ($$\stackrel{2n}{n}$$) is even when n $$\geq1$$

2. Relevant equations

as a hint they gave me this identity:
$$\stackrel{n}{k}$$= (n/k)($$\stackrel{n-1}{k-1}$$)

3. The attempt at a solution

by using that identity i got:

($$\stackrel{2n}{n}$$) = (2n/n) ($$\stackrel{2n-1}{n-1}$$)
= (2) ($$\stackrel{2n-1}{n-1}$$)

i thought anything multiplied by 2 is an even number. but then again this is discrete math. how would i inductively show that this is true?

2. Oct 28, 2009

### HallsofIvy

Staff Emeritus
That's pretty much it. The definition of "even number" is that it is of the form 2k for some integer k. Do you already know that $\left(\begin{array}{c}n\\2i\end{array}\right)$ is always an integer?

3. Oct 28, 2009

### ipitydatfu

oh yeah! I forgot about that! thanks!