IMO Shortlist 1981 problem 8


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2. travnja 2012.
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Take r such that 1\le r\le n, and consider all subsets of r elements of the set \{1,2,\ldots,n\}. Each subset has a smallest element. Let F(n,r) be the arithmetic mean of these smallest elements. Prove that: F(n,r)={n+1\over r+1}.
Izvor: Međunarodna matematička olimpijada, shortlist 1981