What a Proof Is · Medium problem

A student proves "$n^2 + n$ is even for every integer $n$" by writing $n = 2k + 1$ and computing $n^2 + n = 2(2k^2 + 3k + 1)$. The algebra is right. For how many of the integers $1, 2, \ldots, 50$ has the student actually given a reason?