I am not sure where to start with this problem.
If n is a positive integer and n > 1, prove that C(n, 2) + C(n-1, 2) is a perfect square.
Any hints would be appreciated.
Hello, MasterShake!
I am not sure where to start with this problem. . . . . really?
If $\displaystyle n$ is a positive integer and $\displaystyle n > 1$,
prove that: .$\displaystyle C(n, 2) + C(n-1, 2)$ is a perfect square.
Do you know what those C-expressions mean?
If you do, just do the algebra . . .
$\displaystyle C(n,2) +C(n-1,2) \;=\;\frac{n!}{2!(n-2)!} + \frac{(n-1)!}{2!(n-3)!} \;=\;\frac{n(n-1)}{2} + \frac{(n-1)(n-2)}{2}$ . . . etc.
Even after trying to plug the equation I still am unsure how to set up the proof.
C(n, r) = n! / r!(n-r)!
shouldn't the bases of both equations be 2!(n-2)!