1970 Canadian MO Problems/Problem 9

Problem

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.