Proof Writing & Problem Solving · Easy problem

People arrive at a party one at a time, and each newcomer shakes hands with everyone already there. If $H(n)$ is the number of handshakes once $n$ people have arrived, then $H(1) = 0$ and $H(n + 1) = H(n) + n$, and induction gives $H(n) = \dfrac{n(n-1)}{2}$. How many handshakes are there once $12$ people have arrived?