$\sum_{i=1}^{n}i^{2} = \binom{n+1}{2}+2\binom{n+1}{3}$
I imagine the total number of ways of forming at least 1 pair of couple from n males and n females, which should be described by the L.H.S. However, I don't know how to find a different way to count the same number that match the R.H.S.
Are there any tricks when doing combinatorial proofs?
