CMO 1970 Problem 9

Let $f(n)$ be the sum of the first $n$ terms of the sequence $$0, 1,1, 2,2, 3,3, 4,4, 5,5, 6,6, \ldots .$$ a) Give a formula for $f(n)$ . b) Prove that $f(s+t)-f(s-t)=st$ where $s$ and $t$ are positive integers and $s>t$ .