Show that:
$\binom{n+1}{2} = \binom{n}{2} + n$
I think I am supposed to use the number of Combinations formula:
$ \binom{n}{k} = \frac{n(n-1)(n-2)(n-k+1))}{k(k-1)(k-2)..1)} = \frac{n!}{k!(n-k)!}$
I tried to use the formula on the LHS and got this:
$\frac{(n+1)!}{2(n-1)}$