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Simple sequence

Source: Canada 1970, Problem 9

May 14, 2006
algebra unsolvedalgebra

Problem Statement

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