RO-TST 2005 Problem 6

A sequence of real numbers $\{a_n\}_n$ is called a bs sequence if $a_n = |a_{n+1} - a_{n+2}|$ , for all $n\geq 0$ . Prove that a bs sequence is bounded if and only if the function $f$ given by $f(n,k)=a_na_k(a_n-a_k)$ , for all $n,k\geq 0$ is the null function.

Mihai Baluna - ISL 2004