Take
such that
, and consider all subsets of
elements of the set
. Each subset has a smallest element. Let
be the arithmetic mean of these smallest elements. Prove that:
%V0
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: $$F(n,r)={n+1\over r+1}.$$
Školjka