- #1

Coldie

- 84

- 0

If n is a positive integer and n > 1, prove that nC2 + (n-1)C2 is a perfect square.

Now, expanded, this is what they look like...

[TEX]\frac{n!}{2!(n-2)!} + \frac{(n-1)!}{2!(n-3)!}[/TEX]

I'm not sure whether to multiply by the denominators or whether I'm simply supposed to try to simplify each one on its own, or a combination of the two. Moreover, I'm certain I'll still have at least one factorial left when I'm through, and how can I prove that any function with a factorial in it is a perfect square? Could someone give me a nudge in the right direction?