1970 Canadian MO Problems/Problem 9

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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 $f(s+t)-f(s-t)=s$t where $s$ and $t$ are positive integers and $s>t$.

Solution

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