1. ## verify uh...

Greetings math gods. This class is killing me. I don't mind when questions involve numbers but I hate stuff like this.

Verify: $\frac{n!} { 2!(n-2)!} = \frac{k!}{ 2!(k-2)!} + k(n-k) +\frac{ (n-k)!}{2!(n-k-2)!}
$

Note: the original question was use the factorial definition of C(m,r) to verify that:

C(n,2) = C(k,2) + k(n-k) + C(n-k,2) 1 <= k <= n

I really have no idea where to begin. How do you manipulate this ?

2. Originally Posted by billym
Greetings math gods. This class is killing me. I don't mind when questions involve numbers but I hate stuff like this.

Verify: $\frac{n!} { 2!(n-2)!} = \frac{k!}{ 2!(k-2)!} + k(n-k) +\frac{ (n-k)!}{2!(n-k-2)!}
$

Note: the original question was use the factorial definition of C(m,r) to verify that:

C(n,2) = C(k,2) + k(n-k) + C(n-k,2) 1 <= k <= n

I really have no idea where to begin. How do you manipulate this ?
LHS = $\frac{n(n-1)}{2}$.

RHS = $\frac{k(k-1)}{2} + k(n-k) + \frac{(n-k)(n-k-1)}{2}$.

Your job is to further simply the RHS and hence show that it's equal to the LHS.