Numbers in a sequence
Source: Cono sur Olympiad 1996 P4
October 7, 2017
algebracombinatorics
Problem Statement
The sequence where have number zero and numbers one.
If we choose two or more numbers in this sequence(but not the all numbers) and substitute one number by arithmetic mean of the numbers selected, we obtain a new sequence with numbers!!!
Show that, we can repeat this operation until we have all numbers are equal
Note: It's not necessary to choose the same quantity of numbers in each operation!!!