Suppose  a_0, a_1, ..., a_n, ...  are positive integers, and  a_0 < a_1 < ... < a_n < ... 

Prove there's a unique  n  >= 1, with  

a_n < (a_0+...+a_n) / n  <= a_(n+1). 

>= means "greater than or equal"

<= means "less than or equal".

_ denotes a subscript. 

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