# Proof that expression is integer [duplicate]

hi guys can you help me with this?

# $$\frac{(2n)!}{2^nn!}$$

## marked as duplicate by user940, user147263, colormegone, Leucippus, davidlowryduda♦Aug 23 '15 at 4:21

If $n=1$ then $(2n)!/2^{n}n! = 1$. Let $n \geq 1$. If $(2n)!/2^{n}n! = k$ for some $k \in \mathbb{N}$, then $$\frac{(2n+2)!}{2^{n+1}(n+1)!} = \frac{(2n+2)(2n+1)(2n)!}{(2n+2)2^{n}n!} = (2n+1)k \in \mathbb{N},$$ qed.