If i suppose that is valid,
then i want to show that is valid by using my assumption. But i can't find a way to do this.
Maybe this is totally wrong way to do it.
Don't forget to show the result for n=1 and n=2.
Since and then . Intuitively, the result is quite clear: if we take two points between 0 and 1, their middle will be between 0 and 1.